Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584836 | Journal of Algebra | 2014 | 10 Pages |
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