On the Matlis reflexive modules

R. Naghipour, K. Bahmanpour, M. Sedghi

Let (R, m) denote a complete local ring and let M be a Matlis reflexive R-module of positive dimension. The purpose of this article is to show that for every minimal element p of AssR(M), the Rp-module Mp has finite length. As a consequence, we provide a new proof of Enochs' Theorem, i.e., M is Matlis reflexive if and only if it has a finitely generated submodule N such that M/N is Artinian. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 101-108