Paper
A relative version of Bass' theorem about finite-dimensional algebras
Authors
Leonid Positselski
Abstract
As a special case of Bass' theory of perfect rings, one obtains the assertion that, over a finite-dimensional associative algebra over a field, all flat modules are projective. In this paper we prove the following relative version of this result. Let be a homomorphism of associative rings such that is a finitely generated projective right -module. Then every flat left -module is a direct summand of an -module filtered by -modules induced from flat left -modules . In other words, a left -module is cotorsion if and only if its underlying left -module is cotorsion. The proof is based on the cotorsion periodicity theorem.