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Introduction

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Book cover Factoring Ideals in Integral Domains

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

Abstract

In this introductory chapter we introduce several variations on factoring ideals into finite products of prime ideals. For example, a domain has radical factorization if each ideal can be factored as a finite product of radical ideals. Such domains are also known as SP-domains. A domain has weak factorization if each nonzero nondivisorial ideal can be factored as the product of its divisorial closure and a finite product of maximal ideals. If one can always have such a factorization where the maximal ideals are distinct, then the domain has strong factorization. Finally, a domain has pseudo-Dedekind factorization if each nonzero noninvertible ideal can be factored as the product of an invertible ideal and a finite product of pairwise comaximal prime ideals with at least one prime in the product. In addition, if each invertible ideal has such a factorization, then the domain has strong pseudo-Dedekind factorization.

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Authors and Affiliations

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

    Marco Fontana

  2. Mathematics and Statistics, University of North Carolina, Charlotte, NC, USA

    Evan Houston & Thomas Lucas

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  1. Marco Fontana
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  2. Evan Houston
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Fontana, M., Houston, E., Lucas, T. (2012). Introduction. In: Factoring Ideals in Integral Domains. Lecture Notes of the Unione Matematica Italiana, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31712-5_1

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