Factoring ideals in integral domains [electronic resource] /
Fontana, Marco.author.
Houston, Evan.author.
Lucas, Thomas.author.
Unione matematica italiana.
This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years.  Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals.  Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.
Description based upon print version of record.
Factoring Ideals in Integral Domains; Preface; Contents; Chapter 1 Introduction; Chapter 2 Sharpness and Trace Properties; 2.1 h-Local Domains; 2.2 Sharp and Double Sharp Domains; 2.3 Sharp and Antesharp Primes; 2.4 Trace Properties; 2.5 Sharp Primes and Intersections; Chapter 3 Factoring Ideals in Almost Dedekind Domains and Generalized Dedekind Domains; 3.1 Factoring with Radical Ideals; 3.2 Factoring Families for Almost Dedekind Domains; 3.3 Factoring Divisorial Ideals in Generalized Dedekind Domains; 3.4 Constructing Almost Dedekind Domains
Chapter 4 Weak, Strong and Very Strong Factorization4.1 History; 4.2 Weak Factorization; 4.3 Overrings and Weak Factorization; 4.4 Finite Divisorial Closure; Chapter 5 Pseudo-Dedekind and Strong Pseudo-Dedekind Factorization; 5.1 Pseudo-Dedekind Factorization; 5.2 Local Domains with Pseudo-Dedekind Factorization; 5.3 Strong Pseudo-Dedekind Factorization; 5.4 Factorization and the Ring R(X); Chapter 6 Factorization and Intersections of Overrings; 6.1 h-Local Maximal Ideals; 6.2 Independent Pairs of Overrings; 6.3 Jaffard Families and Matlis Partitions; 6.4 Factorization Examples
Symbols and DefinitionsReferences; Index
Includes bibliographical references and index.
This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years.  Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals.  Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.
Algebra.
Commutative algebra.
Commutative rings.
Algebraic geometry.
Number theory.
Algebra.
Commutative Rings and Algebras.
Algebraic Geometry.
Number Theory.
Lecture Notes of the Unione Matematica Italiana