A criterion for reflexivity of modules

TL;DR

This paper establishes a criterion for when finitely generated modules over certain rings are reflexive, showing that isomorphism to their double dual implies reflexivity under mild conditions.

Contribution

It provides a new criterion linking module isomorphism to its double dual with reflexivity for modules over rings with mild assumptions.

Findings

Reflexivity characterized by isomorphism to double dual

Applicable to modules over rings with mild assumptions

Advances understanding of module duality properties

Abstract

Let $M$ be a finitely generated module over a ring $\Lambda$. With certain mild assumptions on $\Lambda$, it is proven that $M$ is a reflexive $\Lambda$-module, once $M \cong M^{**}$ as a $\Lambda$-module.