arXiv subjects

Mohammad Eghbali

Publications and source records attributed to Mohammad Eghbali.

3 recordsLinked to original sources

arXiv2026

Regularity, local cohomology and injective modules under contracting endomorphisms

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 $ϕ: R \to R$ be such an endomorphism, and denote by $^ϕR$ the ring $R$ endowed with the left $R$-module structure induced by $ϕ$. We employ the functor $\text{Hom}_R(^ϕR,-)$ to derive new characterizations of regular rings. Furthermore, we examine the behavior of the functor $(-) \otimes_R {^ϕ}R$ on local cohomology modules and injective modules.

math.AC↗

arXiv2020

On the interplay between the Frobenius functor and its dual

For a commutative Noetherian ring $R$ of prime characteristic, denote by $^{f}R$ the ring $R$ with the left structure given by the Frobenius map. We develop Thomas Marley's work on the property of the Frobenius functor $\F(-) = - \otimes_R {^f}R$ and show the interplay between $\F$ and its dual $\widetilde{\F}(-) = \Hom_R({}^{f}R, -)$ which is introduced by Jürgen Herzog.

math.AC↗

arXiv2017

Hom and Ext, Revisited

Let $R$ be a commutative Noetherian local ring and $M,N$ be finitely generated $R$-modules. We prove a number of results of the form: if $\mbox{Hom}_R(M,N)$ has some nice properties and $\mbox{Ext}^{1 \leq i \leq n}_R(M,N)=0$ for some $n$, then $M$ (and sometimes $N$) must be be close to free. Our methods are quite elementary, yet they suffice to give a unified treatment, simplify, and sometimes extend a number of results in the literature.

math.AC↗