Non-commutative regular local rings of dimension 2. II
type: Item
instance of: scholarly article
title: Non-commutative regular local rings of dimension 2. II
zbMATH Open document ID: 0668.16006
DOI: 10.1016/0021-8693(88)90028-2
author: A. W. Chatters
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: In an earlier paper [ibid. 115, No.1, 219-237 (1988; Zbl 0648.16010)] the author constructed a prime ring T by localising at the maximal Ore set of regular elements modulo P, where P is a prime ideal of a noetherian ring R that is generated by two elements x,y such that y is a nonzero divisor, \(yR=Ry\), x is a nonzero divisor modulo yR and \(P=xR+yR=Rx+Ry\). He established various properties of T and in the present paper continues this theme. The Jacobson radical of T is yT and T/yT is semiprime; the number of prime ideals minimal over yT is denoted n(T). Two rings R and S are said to be matrix equivalent if there are rings \(R=R_ 0,R_ 1,...,R_ m=S\) such that for each pair \(\{R_ i,R_{i+1}\}\) one ring is a full matrix ring over the other. One of the main results in the paper is that the ring T is matrix equivalent to an n(T)\(\times n(T)\) tiled matrix ring over a domain D with properties similar to T but \(n(D)=1\).
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 4093672
zbMATH Keywords: prime ring
zbMATH Keywords: maximal Ore set of regular elements
zbMATH Keywords: noetherian ring
zbMATH Keywords: Jacobson radical
zbMATH Keywords: number of prime ideals
zbMATH Keywords: full matrix ring
zbMATH Keywords: tiled matrix ring
reviewed by: T. H. Lenagan
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90028-2
OpenAlex ID: W2062811229
cites work: Q3890834
cites work: Representation of tiled matrix rings as full matrix rings
cites work: Endomorphism Rings of Torsionless Modules
description: scientific article; zbMATH DE number 4093672