On regular subdirect products of simple Artinian rings

Chen-Lian Chuang and Pjek-Hwee Lee

Vol. 142 (1990), No. 1, 17–21

DOI: 10.2140/pjm.1990.142.17

Abstract

We construct a counterexample to settle simultaneously the following questions all in the negative: (1) Is a regular subdirect product of simple artinian rings unit-regular? (2) If R is a regular ring such that every nonzero ideal of R contains a nonzero ideal of bounded index, is R unit-regular? (3) Is a regular ring with a Hausdorff family of pseudo-rank functions unit-regular? (4) If R is a regular ring which contains no infinite direct sum of nonzero pairwise isomorphic right ideals, is R unit-regular? (5) Is a regular Schur ring unit-regular?

Mathematical Subject Classification 2000

Primary: 16E50

Milestones

Received: 10 January 1988

Published: 1 March 1990