Narrow Results

The purpose of this paper is to examine the freeness of nonzero reflexive modules M and N over a regular local ring R, under the condition is zero.

Let $A$ be an Artin algebra. It is well known that $A$ is selfinjective if and only if every finitely generated $A$-module is reflexive. In this paper, we pose and motivate the question whether an algebra $A$ is selfinjective if and only if every simple module is reflexive. We give a positive answer to this question for large classes of algebras which include for example all Gorenstein algebras and all QF-3 algebras.

In this paper, we introduce the notion of Δ′-reflexive modules. We investigate the reflexive modules with respect to a partial cotilting (bi)module and obtain a connection between Δ′-reflexive modules and Cogen(P)-linearly compact modules. The main results generalize the results on reflexive modules with respect to a cotilting bimodule.