Neat rings
type: Item
instance of: scholarly article
title: Neat rings
zbMATH Open document ID: 1095.13025
author: Warren Wm. McGovern
published in: Journal of Pure and Applied Algebra
publication date: 2006-03-29T00:00:00Z
review text: A ring is clean if every element is a sum of a unit and an idempotent. A ring is neat if every proper factor of it is clean. The paper has several results on neat rings: (1) a collection of several equivalent conditions for a commutative ring to be clean. (2) classification of neatness for some classes of rings: (a) rings over which every finitely generated module is a direct sum of cyclics, (b) Bézout domains (in terms of their group of divisibility); (3) Other examples of neat rings: (a) every h-local domain; (b) every domain with Krull dimension. Besides these, the last two sections of the paper contain generalizations on rigid extension of lattice-ordered abelian groups and relating properties of the additive group of continuous functions of a topological space to its topology. These two sections are independent of the rest of the paper.
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 13F99
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 5016243
zbMATH Keywords: clean ring
zbMATH Keywords: Bézout domain
zbMATH Keywords: group of divisibility
zbMATH Keywords: rigid extension of lattice-ordered groups
MaRDI profile type: Publication
full work available at URL: j.jpaa.2005.07.012
OpenAlex ID: W4213046853
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DOI: 10.1016/J.JPAA.2005.07.012
description: scientific article; zbMATH DE number 5016243