Article ID Journal Published Year Pages File Type
4584836 Journal of Algebra 2014 10 Pages PDF
Abstract

Let R be a left hereditary ring. We show that if the left cotorsion envelope of R is countably generated, then R is a semilocal ring. In particular, we deduce that is finitely generated if and only if R is a semiperfect cotorsion ring. Our proof is based on set theoretical counting arguments. We also discuss some possible extensions of this result.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory