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Mathematics - Algebra | Factoring Ideals in Integral Domains

Factoring Ideals in Integral Domains

Fontana, Marco, Houston, Evan, Lucas, Thomas

2013, VIII, 164 p.

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  • Latest developments in the theory of ideal factorizations - not included in any other recent books Particularly useful to young researchers in commutative algebra Emphasizes historical development of the subject

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.

Content Level » Research

Keywords » 13AXX, 13CXX, 13GXX, 14A05, 11AXX - Dedekind domain - h-local domain - ideal factorization - trace property

Related subjects » Algebra - Number Theory and Discrete Mathematics

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