On regular subdirect products of simple Artinian rings
Chen-Lian Chuang, Pjek-Hwee Lee · Pacific Journal of Mathematics · 1990
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?