Finiteness in regular rings
type: Item
instance of: scholarly article
title: Finiteness in regular rings
zbMATH Open document ID: 0794.16012
DOI: 10.1007/BF02259851
author: D. V. Tyukavkin
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
review text: The paper is mainly concerned with the solution of the following problem. Let \(R\) be a directly finite regular ring and \(M\) its maximal ideal. Is the factor ring \(R/M\) directly finite? The paper gives an example of a directly finite regular ring whose unique simple factor is not directly finite. Moreover, the ring in question has infinite stable range, which is of independent interest.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 19B10
Mathematics Subject Classification ID: 16K40
zbMATH DE Number: 536660
zbMATH Keywords: directly finite regular ring
zbMATH Keywords: maximal ideal
zbMATH Keywords: simple factor
zbMATH Keywords: stable range
MaRDI profile type: Publication
cites work: Q3328689
cites work: Holomorphy of an arbitrary unbounded mapping of a plane domain into the plane, preserving angles along a system of rays
cites work: On regular rings with stable range 2
cites work: On regular subdirect products of simple Artinian rings
cites work: Perspectivity and cancellation in regular rings
cites work: On a class of regular rings that are elementary divisor rings
description: scientific article; zbMATH DE number 536660