A relative version of Bass’ theorem about finite-dimensional algebras
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 R ⟶ A R\longrightarrow A be a homomorphism of associative rings such that A A is a finitely generated projective right R R -module. Then every flat left A A -module is a direct summand of an A A -module filtered by A A -modules A ⊗ R F A\otimes _{R}F induced from flat left R R -modules F F . In other words, a left A A -module is cotorsion if and only if its underlying left R R -module is cotorsion. The proof is based on the cotorsion periodicity theorem.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 6
- Pages
- 2369–2381
- Publication date
- 14 January 2026
- Language
- EN