Rings whose kernel functors are linearly ordered
type: Item
instance of: scholarly article
title: Rings whose kernel functors are linearly ordered
zbMATH Open document ID: 0595.16024
author: Ana M. da Rocha de Viola-Prioli
author: Jorge E. Viola-Prioli
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Rings whose kernel functors are linearly ordered are introduced here as a new non-commutative analogue of valuation rings: they include previous generalizations and coincide with them when commutativity is assumed. Unlike other generalized valuation rings, the defining property transfers nicely to matrix rings, thus enabling us to treat questions in a broader context. A semigroup structure imposed on the lattice of kernel functors is analyzed and the article concludes by examining when that semigroup can be thought of as the semigroup of a valuation ring. In addition, several examples are discussed throughout.
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 13A18
zbMATH DE Number: 3957362
zbMATH Keywords: generalized valuation rings
zbMATH Keywords: matrix rings
zbMATH Keywords: lattice of kernel functors
zbMATH Keywords: semigroup of a valuation ring
MaRDI profile type: Publication
full work available at URL: pjm.1988.132.21
OpenAlex ID: W2038820715
DOI: 10.2140/PJM.1988.132.21
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description: scientific article; zbMATH DE number 3957362