Year: 2026
Type: article
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.
DOI: 10.1090/proc/17632
Author: Leonid Positselski
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417491560