Perinormal rings with zero divisors

Tiberiu Dumitrescu; Anam Rani

arXiv:1609.09216·math.AC·September 30, 2016

Perinormal rings with zero divisors

Tiberiu Dumitrescu, Anam Rani

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TL;DR

This paper generalizes the concept of perinormal domains to rings with zero divisors, identifying conditions under which such rings are perinormal, including Pr"ufer and Marot Krull rings.

Contribution

It introduces the notion of perinormality for rings with zero divisors, extending prior domain-focused concepts to a broader class of rings.

Findings

01

Pr"ufer rings are perinormal.

02

Marot Krull rings are perinormal.

03

Extension of perinormality concept to rings with zero divisors.

Abstract

We extend to rings with zero-divisors the concept of perinormal domain introduced by N. Epstein and J. Shapiro. A ring $A$ is called perinormal if every overring of $A$ which satisfies going down over $A$ is $A$ -flat. The Pr\"ufer rings and the Marot Krull rings are perinormal.

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Taxonomy

TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models