cohen macaulay modules co torsion pairs and virtually gorenstein algebras abstract we use torsion pairs in stable categories and cotorsion pairs in modules categories to study in general infinitely generated cohen macaulay modules and a generalization of modules of finite projective or injective dimension over an artin algebra we concentrate our investigation to the study of virtually gorenstein algebras which provide a common generalization of gorenstein algebras and algebras of finite representation or cohen macaulay type this class of algebras on the one hand has rich homological structure and satisfies several representation torsion theoretic finiteness conditions and on the other hand it is closed under various operations for instance derived equivalences and stable equivalences of morita type in addition virtual gorensteinness provides a useful tool for the study of the gorenstein symmetry conjecture and modified versions of the telescope conjecture for module or stable categories

proper resolutions and gorenstein categories abstract let a be an abelian category and c an additive full subcategory of a we provide a method to construct a proper c resolution resp coproper c coresolution of one term in a short exact sequence in a from that of the other two terms by using these constructions we answer affirmatively an open question on the stability of the gorenstein category g c posed by sather wagstaff sharif and white and also prove that g c is closed under direct summands in addition we obtain some criteria for computing the c dimension and the g c dimension of an object in a

a foundation on semigroups of operators defined on the set of triangular fuzzy numbers and its application to fuzzy fractional evolution equations abstract in this article we study the strongly continuous semigroups of fuzzy valued operators defined on the space of triangular fuzzy numbers new notions of fuzzy infinitesimal generators and fuzzy resolvent operators of fuzzy semigroups are established in the sense of the generalized hukuhara difference a hille yosida like theorem in the framework of fuzzy metric space is investigated we demonstrate the efficiency of theoretical results by studying the existence of mild solutions of fuzzy nonlinear fractional evolution equations

fractional calculus for interval valued functions abstract we use a generalization of the hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval valued functions the properties of riemann liouville fractional integral riemann liouville fractional derivative and caputo fractional derivative for interval valued functions are investigated several examples are presented to illustrate the concepts and results

nonlinear iteration semigroups of fuzzy cauchy problems in this paper we introduce an iteration semigroup of a nonlinear fuzzy valued function we show that the iterates converge and the limit function called the fuzzy exponential function is a solution to an autonomous fuzzy cauchy problem

a categorification of biclosed sets of strings abstract we consider a closure space known as biclosed sets of strings of a gentle algebra of finite representation type palu pilaud and plamondon proved that the collection of all biclosed sets of strings forms a lattice and moreover that this lattice is congruence uniform many interesting examples of finite congruence uniform lattices may be represented as the lattice of torsion classes of an associative algebra we introduce a generalization the lattice of torsion shadows and we prove that the lattice of biclosed sets of strings is isomorphic to a lattice of torsion shadows when every indecomposable module over the gentle algebra is a brick finite congruence uniform lattices admit an alternate partial order known as the core label order in many cases the core label order of a congruence uniform lattice is isomorphic to a lattice of wide subcategories of an associative algebra analogous to torsion shadows we introduce wide shadows and prove that the core label order of the lattice of biclosed sets is isomorphic to a lattice of wide shadows

on the decision problem for mell in this short paper i will exhibit several mistakes in the recent attempt by bimbo to prove the decidability of the multiplicative exponential fragment of linear logic mell in fact the main mistake is so serious that there is no obvious fix and therefore the decidability of mell remains to be an open problem as a side effect this paper contains a complete syntactic proof of the decidability of the relevant version of mell called rmell in this paper that is the logic obtained from mell by replacing the linear logic contraction rule by a general unrestricted version of the contraction rule this proof can also be found with a small error in bimbo s work and a semantic proof has been given by okada and terui

auslander gorenstein algebras from serre formal algebras via replication abstract we introduce a new family of algebras called serre formal algebras they are iwanaga gorenstein algebras for which applying any power of the serre functor on any indecomposable projective module the result remains a stalk complex typical examples are given by higher hereditary algebras and self injective algebras it turns out that other interesting algebras such as higher canonical algebras are also serre formal starting from a serre formal algebra we consider a series of algebras called the replicated algebras given by certain subquotients of its repetitive algebra we calculate the self injective dimension and dominant dimension of all such replicated algebras and determine which of them are minimal auslander gorenstein i e when the two dimensions are finite and equal to each other in particular we show that there exist infinitely many minimal auslander gorenstein algebras in such a series if and only if the serre formal algebra is twisted fractionally calabi yau we apply these results to a construction of algebras from yamagata 29 called sgc extensions given by iteratively taking the endomorphism ring of the smallest generator cogenerator we give a sufficient condition so that the sgc extensions and replicated algebras coincide consequently in such a case we obtain explicit formulae for the self injective dimension and dominant dimension of the sgc extension algebras

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

on the solution of fuzzy fractional optimal control problems with the caputo derivative abstract this paper presents an extension to fractional optimal control problems with ambiguity as the ambiguity is modeled with fuzzy method we encounter with a fuzzy fractional optimal control problem the objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index here the fractional derivative is described in the caputo sense to find the solution first we state some definitions and prove some required theorems then we employ the obtained result to determine the necessary conditions furthermore we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions finally some examples are presented for more illustration of the subject

standardly stratified algebras and tilting abstract the concept of the characteristic tilting module and of the ringel dual for quasi hereditary algebras is generalized for the setting of standardly stratified algebras

tilting categories with applications to stratifying systems abstract in the study of standardly stratified algebras and stratifying systems we find an object which is either a tilting module or one whose properties strongly remind us of a tilting module this tilting module appeared already in dlab and ringel s work on quasi hereditary algebras see v dlab c m ringel the module theoretical approach to quasi hereditary algebras in repr theory and related topics in london math soc lecture note ser 168 1992 200 224 and c m ringel the category of modules with good filtrations over a quasi hereditary algebra has almost split sequences math z 208 1991 209 223 also this tilting module appears on the work on standardly stratified algebras of i agoston d happel e lukacs and l unger and in the paper of m i platzeck and i reiten see i agoston d happel e lukacs l unger standardly stratified algebras and tilting j algebra 226 2000 144 160 and m i platzeck i reiten modules of finite projective dimension for standardly stratified algebras comm algebra 29 3 2001 973 986 inspired by them we introduce the notion of tilting category in order to give a unified approach of these situations for stratifying systems to do so we use the ideas of m auslander o buchweitz and i reiten related to approximation theory see m auslander r o buchweitz the homological theory of maximal cohen macaulay approximations mem soc math fr n s 38 1989 5 37 m auslander i reiten applications of contravariantly finite subcategories adv math 86 1991 111 152

syzygy modules for quasi k gorenstein rings abstract let be a right quasi k gorenstein ring for each dth syzygy module m in mod where 0 d k 1 we obtain an exact sequence 0 b m p c 0 in mod with the properties that it is dual exact p is projective c is a d 1 st syzygy module b is a dth syzygy of ext op d 1 tr m and the right projective dimension of b is less than or equal to d 1 we then give some applications of such an exact sequence as follows 1 we obtain a chain of epimorphisms concerning m and by dualizing it we then get the spherical filtration of auslander and bridger for m 2 we get auslander and bridger s approximation theorem for each reflexive module in mod op 3 we show that for any 0 d k 1 each dth syzygy module in mod has an evans griffith presentation as an immediate consequence of 3 we have that if is a commutative noetherian ring with finite self injective dimension then for any non negative integer d each dth syzygy module in mod has an evans griffith presentation which generalizes an evans and griffith s result to much more general setting

standard stratifications of ei categories and alperin s weight conjecture abstract we characterize the finite ei categories whose representations are standardly stratified with respect to the natural preorder on the simple representations the orbit category of a finite group with respect to any set of subgroups is always such a category taking the subgroups to be the p subgroups of the group we reformulate alperin s weight conjecture in terms of the standard and proper costandard representations of the orbit category we do this using the properties of the ringel dual construction and a theorem of dlab which have elsewhere been described for standardly stratified algebras where there is a partial order on the simple modules we indicate that these results hold in the generality of an algebra whose simple modules are preordered rather than partially ordered

auslander gorenstein algebras and precluster tilting abstract we generalize the notions of n cluster tilting subcategories and selfinjective algebras into n precluster tilting subcategories and n selfinjective algebras where we show that a subcategory naturally associated to n precluster tilting subcategories has a higher auslander reiten theory furthermore we give a bijection between n precluster tilting subcategories and n minimal auslander gorenstein algebras which is a higher dimensional analog of auslander solberg correspondence 8 as well as a gorenstein analog of n auslander correspondence 22 the auslander reiten theory associated to an n precluster tilting subcategory is used to classify the n minimal auslander gorenstein algebras into four disjoint classes our method is based on relative homological algebra due to auslander solberg

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

algebras with irreducible module varieties i abstract we call a finite dimensional k algebra a geometrically irreducible if for all d 0 all connected components of the affine scheme of d dimensional a modules are irreducible we show that the geometrically irreducible algebras without loops this includes all algebras of finite global dimension are the hereditary algebras we also show that truncated polynomial rings are the only geometrically irreducible local algebras finally we formulate a conjectural classification of all geometrically irreducible algebras

representation dimensions of triangular matrix algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k t 2 a a 0 a a be the triangular matrix algebra we prove that rep dim t 2 a is at most three if a is dynkin type and rep dim t 2 a is at most four if a is not dynkin type let a 1 a 0 da a be the duplicated algebra of a let t be a tilting a module and t t p be a tilting a 1 module we show that end a 1 t is representation finite if and only if the full subcategory x a y a f x a mod a y a 1 f t a add a of mod t 2 a is of finite type where is the auslander reiten translation and f t a is the torsion free class of mod a associated with t moreover we also prove that rep dim end a 1 t is at most three if a is dynkin type

the decidability of the intensional fragment of classical linear logic intensional classical linear logic mell is proved decidable intensional interlinear logic rll is proved decidable we adapt kripke s method used to prove decidability for some relevance logics the semi relevant rll emerges as a logic superior to mell in this context triple and double inductive proofs of cut theorems are explained in some detail the intensional fragment of classical propositional linear logic combines modalities with contraction free relevance logic adding modalized versions of the thinning and contraction rules this paper provides a proof of the decidability of this logic based on a sequent calculus formulation some related logics and some other fragments of linear logic are also shown decidable

almost split sequences in subcategories let r be a commutative artin ring and let i be an r algebra which is a finitely generated r module in 5 auslander and reiten introduced the notion of an almost split sequence in mod a the category of finitely generated modules over a and the existence and uniqueness of such short exact sequences were established there the theory of almost split sequences developed further and similar results for certain subcategories of mod i were proved by bautista and martinez 8 and roggenkamp 9 the main purpose of this paper is to develop a more general theory for subcategories of mod i having almost split sequences which has the previous examples as special cases notions closely related to that of almost split sequences are those of minimal left and right almost split morphisms these notions were introduced in 61 for mod i and further developed in 7 for subcategories of mod ii this paper is based upon 7 and we therefore use the same notations and conventions as used there we now give some definitions and then proceed to describe the content of the paper section by section let c be a subcategory of mod ii then a morphism g b c in c is said to be a right almost split morphism in c if i g is not a splittable epimorphism and ii whenever there is a nonsplittable epimorphism h c c in c there exists an h c b such that gh h dually a morphismfi a f b in c is said to be left almost split if i f is not a splittable monomorphism and ii whenever there is a nonsplittable monomorphism h a a there exists an h b a such that h f h we say that c has right almost split morphisms if for all indecomposable objects

higher nakayama algebras i construction we introduce higher dimensional analogues of the nakayama algebras from the viewpoint of iyama s higher auslander reiten theory more precisely for each nakayama algebra a and each positive intege

triangle singularities ade chains and weighted projective lines abstract we study the singularity category of the triangle singularity f x a y b z c or s k x y z f attached to the weighted projective line x given by the weight triple a b c by investigating the stable category vect x of vector bundles on x obtained from the category of vector bundles by factoring out all the line bundles we show that vect x is fractional calabi yau whose cy dimension is a function of the euler characteristic of x and establish the existence of a tilting object having the shape of an a 1 b 1 c 1 cuboid the weight types 2 a b yield an explanation of happel seidel symmetry for a class of important nakayama algebras further the weight sequence 2 3 p corresponds to an ade chain the e n chain extrapolating the exceptional dynkin cases e 6 e 7 and e 8 to a whole sequence of triangulated categories

endomorphism algebras of tilting modules over m replicated algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k and let a m be the m replicated algebra of a in this paper we investigate the structure properties of the endomorphism algebras of tilting modules of a m and prove that all the endomorphism algebras of tilting modules of a m can be realized as the iterated endomorphism algebras of bb tilting modules that is for each pair of basic tilting a m modules t 1 and t 2 there exists a series of finite dimensional algebras 0 1 s which are the endomorphism algebras of some basic tilting a m modules and for each i there is a bb tilting i module m i such that 0 end a m t 1 i end i 1 m i 1 for 1 i s and end a m t 2 end s m s

gorenstein projective modules and symmetric recollements we introduce compatible bimodules if m is a compatible a b bimodule then the gorenstein projective modules over algebra am0b are explicitly described and if is gorenstein then this description implies that m is compatible as an application if m is compatible then there is a left recollement of the stable category gp and if is gorenstein and ma is projective then there is a symmetric recollement of the singularity category dsgb

the transpose of modules relative to subcategories abstract let r be a left noetherian ring and s a right noetherian ring and let x be a subcategory of finitely generated left r modules and b s r a finite r s bimodule as a generalization of the auslander transpose replacing a projective presentation by an x presentation and the functor hom r r by the functor hom r b we introduce the x b transpose of an r module m admitting an x presentation for a suitable subcategory x some useful properties of x b transposes are obtained it is shown that the x b transpose shares many nice properties with the auslander transpose some known results are obtained as corollaries

on arkhipov s and enright s functors we give a description of arkhipov s and joseph s and deodhar mathieu s versions of enright s endofunctors on the category open image in new window associated with a fixed triangular decomposition of a complex finite dimensional semi simple lie algebra in terms of co approximation functors with respect to suitably chosen injective resp projective modules we establish some new connections between these functors for example we show that arkhipov s and joseph s functors are adjoint to each other we also give several proofs of braid relations for arkhipov s and enright s functors

enright s completions and injectively copresented modules let 21 be a finite dimensional simple lie algebra over the complex numbers it is shown that a module is complete or relatively complete in the sense of enright if and only if it is injectively copresented by certain injective modules in the bgg category o let a be the finite dimensional algebra associated to a block of o then the corresponding block of the category of complete modules is equivalent to the category of eae modules for a suitable choice of the idempotent e using this equivalence a very easy proof is given for deodhar s theorem also proved by bouaziz that completion functors satisfy braid relations the algebra eae is left properly and standardly stratified it satisfies a double centralizer property similar to soergel s combinatorial description of o its simple objects their characters and their multiplicities in projective or standard objects are determined

maximal rigid subcategories and cluster tilting subcategories in 2 cy categories abstract let c be a connected hom finite 2 cy triangulated category we prove that if t is a functorially finite maximal rigid subcategory of c without loops in its quiver then t is cluster tilting in particular this gives a positive answer to a conjecture proposed in 5

three results on frobenius categories this paper consists of three results on frobenius categories 1 we give sufficient conditions on when a factor category of a frobenius category is still a frobenius category 2 we show that any frobenius category is equivalent to an extension closed exact subcategory of the frobenius category formed by cohen macaulay modules over some additive category this is an analogue of gabriel quillen s embedding theorem for frobenius categories 3 we show that under certain conditions an exact category with enough projective and enough injective objects allows a natural new exact structure with which the given category becomes a frobenius category several applications of the results are discussed

double centralizer properties dominant dimension and tilting modules double centralizer properties play a central role in many parts of algebraic lie theory soergel s double centralizer theorem relates the principal block of the bernstein gelfand gelfand category o of a semisimple complex lie algebra with the coinvariant algebra i e the cohomology algebra of the corresponding flag manifold schur weyl duality relates the representation theories of general linear and symmetric groups in defining characteristic or via the quantized version in nondefining characteristic in this paper we exhibit algebraic structures behind these double centralizer properties we show that the finite dimensional algebras relevant in this context have dominant dimension at least two with respect to some projective injective or tilting modules general arguments which combine methods from ring theory qf 3 rings and dominant dimension with tools from representation theory approximations tilting modules then imply the validity of these double centralizer properties as well as new ones in contrast to the traditional proofs e g by the fundamental theorems of invariant theory no computations are necessary

from triangulated categories to module categories via localisation we show that the category of finite dimensional modules over the endomorphism algebra of a rigid object in a hom finite triangulated category is equivalent to the gabriel zisman localisation of the category with respect to a certain class of maps this generalises the 2 calabi yau tilting theorem of keller reiten in which the module category is obtained as a factor category to the rigid case

on fuzzy solutions for heat equation based on generalized hukuhara differentiability abstract in this paper a fuzzy heat equation with fuzzy initial values is considered the concept of generalized hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases and also several properties for generalized hukuhara differentiability are obtained on the topics such as switching point the univariate and multivariate fuzzy chain rules fuzzy mean value theorem among others the objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions finally some examples show the behavior of the solutions obtained

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

representation theoretic properties of balanced big cohen macaulay modules let r mathfrak m k be a complete cohen macaulay local ring in this paper we assign a numerical invariant for any balanced big cohen macaulay module called underline mathsf h length among other results it is proved that for a given balanced big cohen macaulay r module m with an mathfrak m primary cohomological annihilator if there is a bound on the underline mathsf h length of all modules appearing in mathsf cm support of m then it is fully decomposable i e it is a direct sum of finitely generated modules while the first brauer thrall conjecture fails in general by a counterexample of dieterich dealing with multiplicities to measure the size of maximal cohen macaulay modules our formalism establishes the validity of the conjecture for complete cohen macaulay local rings in addition the pure semisimplicity of a subcategory of balanced big cohen macaulay modules is settled namely it is shown that r is of finite mathsf cm type if and only if r is an isolated singularity and the category of all fully decomposable balanced big cohen macaulay modules is closed under kernels of epimorphisms finally we examine the mentioned results in the context of cohen macaulay artin algebras admitting a dualizing bimodule omega as defined by auslander and reiten it will turn out that omega gorenstein projective modules with bounded mathsf cm support are fully decomposable in particular a cohen macaulay algebra lambda is of finite mathsf cm type if and only if every omega gorenstein projective module is of finite mathsf cm type which generalizes a result of chen for gorenstein algebras our main tool in the proof of results is gabriel roiter co measure an invariant assigned to modules of finite length and defined by gabriel and ringel this in fact provides an application of the gabriel roiter co measure in the category of maximal cohen macaulay modules

the structure of preenvelopes with respect to maximal cohen macaulay modules abstract this paper studies the structure of special preenvelopes and envelopes with respect to maximal cohen macaulay modules we investigate the structure of them in terms of their kernels and cokernels moreover using this result we also study the structure of special proper coresolutions with respect to maximal cohen macaulay modules over a henselian cohen macaulay local ring

reconstruction of path algebras from their posets of tilting modules let a k be the path algebra of a finite quiver without orientedcycles the set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set we will show here that t a uniquely determines if has no multiple arrows and no isolated vertices

an auslander buchweitz approximation approach to pre silting subcategories in triangulated categories abstract we apply the auslander buchweitz approximation triangles to study pre silting subcategories in a triangulated catego ry t an auslander reiten type correspondence between the class of silting subcategories of t and that of certain covariantly finite subcategories of t is established we introduce a relation on presilting subcategories of t which can be used to obtain another silting subcategory from a given one we also give a bazzoni s characterization for two presilting subcategories satisfying such a relation the results can be used to improve the auslander reiten type correspondence and bazzoni s characterization for small silting complexes established by wei

generalized tilting modules with finite injective dimension let r be a left noetherian ring s be a right noetherian ring and r be a generalized tilting module with s end r we mainly consider the conditions such that l id r 1 in this paper and obtain some characterizations for this inequality further when l id r and r id s are finite we provide the conditions such that r and s are injective as a direct application we get some necessary and sufficient conditions for a gorenstein ring to be a qf ring

upper bounds for the dominant dimension of nakayama and related algebras abstract optimal upper bounds are provided for the dominant dimensions of nakayama algebras and more general algebras a with an idempotent e such that there is a minimal faithful injective projective module ea and such that eae is a nakayama algebra this answers a question of abrar and proves a conjecture of yamagata for monomial algebras

the gorenstein projective modules for the nakayama algebras i abstract the aim of this paper is to outline the structure of the category of the gorenstein projective modules where is a nakayama algebra in addition we are going to introduce the resolution quiver of it provides a fast algorithm in order to obtain the gorenstein projective modules and to decide whether is a gorenstein algebra or not and whether it is cm free or not

a note on abelian quotient categories abstract let c be a triangulated category with a serre functor s and x a non zero contravariantly finite rigid subcategory of c then x is cluster tilting if and only if the quotient category c x is abelian and s x x 2 as an application this result generalizes the work by beligiannis

on modules with trivial self extensions throughout this note all rings will be self basic connected artin algebras over a fixed commutative local artin ring k and all modules will be finitely generated homomorphisms will be written on the opposite side of the scalars by mod a resp a mod we denote the category of all right resp left a modules for an artin algebra a the ordinary duality functor is denoted by d mod a 2 a mod i e d hom f with the minimal injective cogenerator i over k we are interested in the bimodules bta with the following properties

approximations and the little finitistic dimension of artinian rings let r be a ring and let simp r be a representative set of all simple right r modules denote by p the class of all modules which are finitely generated and have finite projective dimension the little finitistic dimension of r is defined by fdim r sup proj dim m m p let a b be the complete cotorsion theory cogenerated by p for each s simp r let fs xs s be a special a precover of s we prove that fdim r max proj dim xs s simp r provided that r is right artinian as a corollary we extend to right artinian rings the well known auslander reiten sufficient condition for finiteness of the little finitistic dimension

mell in the calculus of structures the calculus of structures is a new proof theoretical formalism like natural deduction the sequent calculus and proof nets for specifying logical systems syntactically in a rule in the calculus of structures the premise as well as the conclusion are structures which are expressions that share properties of formulae and sequents in this paper i study a system for mell the multiplicative exponential fragment of linear logic in the calculus of structures it has the following features a local promotion rule no non deterministic splitting of the context in the times rule and a modular proof for the cut elimination theorem further derivations have a new property called decomposition that cannot be observed in any other known proof theoretical formalism

on galois coverings and tilting modules abstract let a be a basic connected finite dimensional algebra over an algebraically closed field k let t be a basic tilting a module with arbitrary finite projective dimension for a fixed group g we compare the set of isoclasses of connected galois coverings of a with group g and the set of isoclasses of connected galois coverings of end a t with group g using the hasse diagram k a see d happel l unger on a partial order of tilting modules algebr represent theory 8 2 2005 147 156 and c riedtmann a schofield on a simplicial complex associated with tilting modules comment math helv 66 1 1991 70 78 of basic tilting a modules we give sufficient conditions on t under which there is a bijection between these two sets these conditions are always verified when a is of finite representation type then we apply these results to study when the simple connectedness of a implies the one of end a t see i assem e n marcos j a de la pena the simple connectedness of a tame tilted algebra j algebra 237 2 2001 647 656 finally using an argument due to w crawley boevey we prove that the type of any simply connected tilted algebra is a tree and that its first hochschild cohomology group vanishes

a survey on fuzzy fractional differential and optimal control nonlocal evolution equations abstract we survey some representative results on fuzzy fractional differential equations controllability approximate controllability optimal control and optimal feedback control for several different kinds of fractional evolution equations optimality and relaxation of multiple control problems described by nonlinear fractional differential equations with nonlocal control conditions in banach spaces are considered

totally reflexive extensions and modules abstract we introduce the notion of totally reflexive extension of rings it unifies gorenstein orders and frobenius extensions we prove that for a totally reflexive extension a module over the extension ring is totally reflexive if and only if its underlying module over the base ring is totally reflexive

the solvability of fuzzy fractional partial differential equations under caputo gh differentiability the foundation of the concepts of fuzzy fractional integral and caputo gh partial for fuzzy valued multivariable functions is defined as a result fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved we present two new results on the existence of two kinds of gh weak solutions of these problems the first result is based on the banach fixed point theorem with the lipschitz condition of functions on the right hand side of equations the second result is based on the nonlinear alternative of the schauder type for fuzzy valued continuous functions without the lipschitz condition moreover we indicate the boundedness and continuous dependence of solutions on the initial data of the problems our models are embedded in the sense of caputo gh differentiability some examples are presented to illustrate the results

auslander type conditions and cotorsion pairs we study the properties of rings satisfying auslander type conditions if an artin algebra satisfies the auslander condition that is is an gorenstein artin algebra then we construct two kinds of subcategories which form functorially finite cotorsion pairs

wakamatsu tilting modules abstract we study a generalization of tilting modules to modules of possibly infinite projective dimension introduced by wakamatsu in j algebra 114 1988 106 114 in particular we characterize these modules in terms of suitable subcategories of finitely generated modules and in terms of cotorsion theories

higher dimensional auslander reiten theory on maximal orthogonal subcategories abstract we introduce the concept of maximal n 1 orthogonal subcategories over artin algebras and orders and develop n 1 dimensional auslander reiten theory on them we give the n auslander reiten translation and the n auslander reiten duality then show the existence of n almost split sequences and n fundamental sequences we give some examples

random fuzzy fractional integral equations theoretical foundations abstract this paper presents mathematical foundations for studies of random fuzzy fractional integral equations which involve a fuzzy integral of fractional order we consider two different kinds of such equations their solutions have different geometrical properties the equations of the first kind possess solutions with trajectories of nondecreasing diameter of their consecutive values on the other hand the solutions to equations of the second kind have trajectories with nonincreasing diameter of their consecutive values firstly the existence and uniqueness of solutions is investigated this is showed by using a method of successive approximations an estimation of error of n th approximation is given also a boundedness of the solution is indicated to show well posedness of the considered theory we prove that solutions depend continuously on the data of the equations some concrete examples of random fuzzy fractional integral equations are solved explicitly

an algorithm for the general petri net reachability problem an algorithm is presented for the general petri net reachability problem it is based on a generalization of the basic reachability tree construction which is made symmetric with respect to the ini

on algebras of finite cohen macaulay type abstract we study artin algebras and commutative noetherian complete local rings r in connection with the following decomposition property of gorenstein projective modules any gorenstein projective module is a direct sum of finitely generated modules we show that the class of algebras enjoying coincides with the class of virtually gorenstein algebras of finite cohen macaulay type introduced in beligiannis and reiten 2007 27 beligiannis 2005 24 thus we solve the problem stated in chen 2008 33 this is proved by characterizing when a resolving subcategory is of finite representation type in terms of decomposition properties of its closure under filtered colimits thus generalizing a classical result of auslander 1976 9 and ringel and tachikawa 1974 63 in the commutative case if r admits a non free finitely generated gorenstein projective module then we show that r is of finite cohen macaulay type iff r is gorenstein and satisfies we also generalize a result of yoshino 2005 68 by characterizing when finitely generated modules without extensions with the ring are gorenstein projective finally we study the stable relative auslander algebra of a virtually gorenstein algebra of finite cohen macaulay type and under the presence of a cluster tilting object we give descriptions of the stable category of gorenstein projective modules in terms of the cluster category associated to the quiver of the stable relative auslander algebra in this setting we show that the cluster category is invariant under derived equivalences

on the classification of higher auslander algebras for nakayama algebras abstract we give new improved bounds for the dominant dimension of nakayama algebras and use those bounds to give a classification of nakayama algebras with n simple modules that are higher auslander algebras with global dimension at least n the classification is then used to extend the results on the inequality for the global dimension of nakayama algebras obtained in 18

the undecidability of second order multiplicative linear logic the multiplicative fragment of second order propositional linear logic is shown to be undecidable

new approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces abstract this study considers the solvability of nonlocal problems for fuzzy differential systems under gh differentiability using some linear transforms we convert partial differential equations into fuzzy integral systems before some similar results are obtained for fuzzy wave equations with nonlocal conditions as a consequence we give some further estimates of the convergence rates of approximation schemes to exact solutions the main tool used in our proofs is based on perov s fixed point principle which is applied to vector valued integral operators these operators appear as the sum of two integral operators where one is fredholm type and the other is of a volterra type that depends on the restriction of the domain the novel feature of this study is that we combine the matrix convergent to zero technique with calculations of fuzzy valued functions in generalized fuzzy metric spaces some examples are presented to demonstrate our theoretical results