Factoring Ideals in Integral Domains

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Factoring Ideals in Integral Domains by Marco Fontana, Evan Houston, Thomas Lucas, Springer Berlin Heidelberg
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Author: Marco Fontana, Evan Houston, Thomas Lucas ISBN: 9783642317125
Publisher: Springer Berlin Heidelberg Publication: September 14, 2012
Imprint: Springer Language: English
Author: Marco Fontana, Evan Houston, Thomas Lucas
ISBN: 9783642317125
Publisher: Springer Berlin Heidelberg
Publication: September 14, 2012
Imprint: Springer
Language: English

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.

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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.

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