Factoring Ideals in Integral Domains

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.

Summary

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.

Product details

• Authors: Marc Fontana, Marco Fontana, Eva Houston, Evan Houston, Thomas Lucas
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 08.06.2012
• EAN: 9783642317118
• ISBN: 978-3-642-31711-8
• No. of pages: 164
• Dimensions: 169 mm x 11 mm x 238 mm
• Weight: 277 g
• Illustrations: VIII, 164 p.
• Series: Lecture Notes of the Unione Matematica Italiana; Lecture Notes of the Unione Matematica Italiana
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Zahlentheorie, Algebra, B, Algebraische Geometrie, Mathematics and Statistics, Algebraic Geometry, Number Theory, Commutative algebra, Commutative rings, Commutative Rings and Algebras