Factoring Ideals in Integral Domains Lecture Notes Of The 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. Annotation This volume provides a wide-ranging survey of, and many new results on, various important typesof 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 Front Matter....Pages i-viii Introduction....Pages 1-3 Sharpness and Trace Properties....Pages 5-38 Factoring Ideals in Almost Dedekind Domains and Generalized Dedekind Domains....Pages 39-70 Weak, Strong and Very Strong Factorization....Pages 71-94 Pseudo-Dedekind and Strong Pseudo-Dedekind Factorization....Pages 95-118 Factorization and Intersections of Overrings....Pages 119-151 Back Matter....Pages 153-164 Provides a survey of, and many results on, various important types of ideal factorization actively investigated by several authors in recent years. In this book, the examples of domains studied include: those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure.