M-Solid Varieties of Algebras [electronic resource] /
Koppitz, Jörg.author.
Denecke, Klaus.author.
M-Solid Varieties of Algebras provides a complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on M-solid varieties of semirings and semigroups. The book aims to develop the theory of M-solid varieties as a system of mathematical discourse that is applicable in several concrete situations. It applies the general theory to two classes of algebraic structures, semigroups and semirings. Both these varieties and their subvarieties play an important role in computer science. A unique feature of this book is the use of Galois connections to integrate different topics. Galois connections form the abstract framework not only for classical and modern Galois theory, involving groups, fields and rings, but also for many other algebraic, topological, ordertheoretical, categorical and logical theories. This concept is used throughout the whole book, along with the related topics of closure operators, complete lattices, Galois closed subrelations and conjugate pairs of completely additive closure operators. Audience This book is intended for researchers in the fields of universal algebra, semigroups, and semirings; researchers in theoretical computer science; and students and lecturers in these fields.
Description based upon print version of record.
Includes bibliographical references and index.
Basic Concepts -- Closure Operators and Lattices -- M-Hyperidentities and M-solid Varieties -- Hyperidentities and Clone Identities -- Solid Varieties of Arbitrary Type -- Monoids of Hypersubstitutions -- M-Solid Varieties of Semigroups -- M-solid Varieties of Semirings.
M-Solid Varieties of Algebras provides a complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on M-solid varieties of semirings and semigroups. The book aims to develop the theory of M-solid varieties as a system of mathematical discourse that is applicable in several concrete situations. It applies the general theory to two classes of algebraic structures, semigroups and semirings. Both these varieties and their subvarieties play an important role in computer science. A unique feature of this book is the use of Galois connections to integrate different topics. Galois connections form the abstract framework not only for classical and modern Galois theory, involving groups, fields and rings, but also for many other algebraic, topological, ordertheoretical, categorical and logical theories. This concept is used throughout the whole book, along with the related topics of closure operators, complete lattices, Galois closed subrelations and conjugate pairs of completely additive closure operators. Audience This book is intended for researchers in the fields of universal algebra, semigroups, and semirings; researchers in theoretical computer science; and students and lecturers in these fields.
Algebra.
Group theory.
Ordered algebraic structures.
Programming languages (Electronic computers).
Mathematical logic.
General Algebraic Systems.
Group Theory and Generalizations.
Order, Lattices, Ordered Algebraic Structures.
Programming Languages, Compilers, Interpreters.
Mathematical Logic and Formal Languages.