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Factoring Ideals in Integral Domains

  • Book
  • © 2013

Overview

Authors:
  1. Marco Fontana

    1. , Dipartimento di Matematica, Università degli Studi Roma Tre, Rome, Italy

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  2. Evan Houston

    1. , Mathematics and Statistics, Univ. of North Carolina at Charlotte, Charlotte, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Thomas Lucas

    1. , Mathematics and Statistics, Univ. of North Carolina at Charlotte, Charlotte, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 14)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 1-3

  3. Sharpness and Trace Properties

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 5-38

  4. Factoring Ideals in Almost Dedekind Domains and Generalized Dedekind Domains

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 39-70

  5. Weak, Strong and Very Strong Factorization

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 71-94

  6. Pseudo-Dedekind and Strong Pseudo-Dedekind Factorization

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 95-118

  7. Factorization and Intersections of Overrings

    • Marco Fontana, Evan Houston, Thomas Lucas
    Pages 119-151

  8. Back Matter

    Pages 153-164
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Keywords

About this book

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.

Authors and Affiliations

  • , Dipartimento di Matematica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  • , Mathematics and Statistics, Univ. of North Carolina at Charlotte, Charlotte, USA

    Evan Houston, Thomas Lucas

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