Factoring Ideals in Integral Domains

✍ Scribed by Marco Fontana, Evan Houston, Thomas Lucas (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 169
• Series: Lecture Notes of the Unione Matematica Italiana 14
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Algebra; Commutative Rings and Algebras; Algebraic Geometry; Number Theory