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arXiv · 2510.02210

Centers of Endomorphism Rings and Reflexivity

Souvik Dey·Justin Lyle
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Abstract

Let $R$ be a local ring and let $M$ be a finitely generated $R$-module. Appealing to the natural left module structure of $M$ over its endomorphism ring and corresponding center $Z(\operatorname{End}_R(M))$, we study when various homological properties of $M$ are sufficient to force $M$ to have a nonzero free summand. Consequences of our work include a partial converse to a well-known result of Lindo describing $Z(\operatorname{End}_R(M))$ when $M$ is faithful and reflexive, as well as some applications to the famous Huneke-Wiegand conjecture.

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Souvik Dey, Justin Lyle. 2025-10-02. Centers of Endomorphism Rings and Reflexivity. https://arxiv.org/abs/2510.02210

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