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arXiv · 2607.13320

Regularity, local cohomology and injective modules under contracting endomorphisms

Kamran Divaani-Aazar·Mohammad Eghbali
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Abstract

This work extends several fundamental results previously established for rings of characteristic $p$ to the broader class of rings that admit a contracting endomorphism. Specifically, let $\phi: R \to R$ be such an endomorphism, and denote by $^{\phi}R$ the ring $R$ endowed with the left $R$-module structure induced by $\phi$. We employ the functor $\text{Hom}_R(^{\phi}R,-)$ to derive new characterizations of regular rings. Furthermore, we examine the behavior of the functor $(-) \otimes_R {^{\phi}}R$ on local cohomology modules and injective modules.

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Kamran Divaani-Aazar, Mohammad Eghbali. 2026-07-14. Regularity, local cohomology and injective modules under contracting endomorphisms. https://arxiv.org/abs/2607.13320

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