Endomorphism Algebras Over Commutative Rings and Torsion in Self Tensor Products
Abstract
Abstract Let R be a commutative Noetherian local ring. We study tensor products involving a finitely generated R -module M through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case where $${\text {End}}_R(M)$$ End R ( M ) has an $$R^*$$ R ∗ -algebra structure, and prove that if M is indecomposable, then $$M \otimes _{{\text {End}}_R(M)} M$$ M ⊗ End R ( M ) M must always have torsion in this case under mild hypotheses.
Fields of Study & Subjects
Rings
Modules
and Algebras
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Acta Mathematica Vietnamica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 51
- Issue
- 3
- Pages
- 353-361
- Publication date
- 13 August 2026
- Language
- EN