Regular rings
type: Item
instance of: scholarly article
title: Regular rings
zbMATH Open document ID: 0652.13001
author: C. Jayaram
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Although there are numerous conditions in the literature which characterize regular rings, these usually involve some sort of (quasi)- ideal-theoretic intersection versus product conditions. In this paper, the set of interesting subsets of a commutative ring R with identity is the set of saturated subsets F (i.e., xy\(\in F\) iff \(x\in F, y\in F)\) of R denoted by S(R), whose properties are explored. Thus, R is regular iff R is semiprime and [a) (the smallest saturated set containing a) has a complement in the lattice S(R) theorem 1); R is Noetherian regular iff S(R) is also a Boolean algebra (theorem 2). Further variations on this theme are also developed in this useful paper.
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 06E99
zbMATH DE Number: 4063227
zbMATH Keywords: lattice of saturated subsets
zbMATH Keywords: regular rings
zbMATH Keywords: Boolean algebra
reviewed by: J. Neggers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4063227