Factoring Ideals in Integral Domains

  • Marco Fontana
  • Evan Houston
  • Thomas Lucas
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 14)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 1-3
  3. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 5-38
  4. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 39-70
  5. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 71-94
  6. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 95-118
  7. Marco Fontana, Evan Houston, Thomas Lucas
    Pages 119-151
  8. Back Matter
    Pages 153-164

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Marco Fontana
    • 1
  • Evan Houston
    • 2
  • Thomas Lucas
    • 3
  1. 1., Dipartimento di MatematicaUniversità degli Studi Roma TreRomeItaly
  2. 2., Mathematics and StatisticsUniv. of North Carolina at CharlotteCharlotteUSA
  3. 3., Mathematics and StatisticsUniv. of North Carolina at CharlotteCharlotteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31712-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31711-8
  • Online ISBN 978-3-642-31712-5
  • Series Print ISSN 1862-9113