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arXiv · 2310.14134

Endomorphism algebras over commutative rings and torsion in self tensor products

Justin Lyle
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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 $\operatorname{End}_R(M)$ has an $R^*$-algebra structure, and prove that if $M$ is indecomposable, then $M \otimes_{\operatorname{End}_R(M)} M$ must always have torsion in this case under mild hypotheses.

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Justin Lyle. 2023-10-21. Endomorphism algebras over commutative rings and torsion in self tensor products. https://arxiv.org/abs/2310.14134

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