Let Λ be an artin algebra. In his seminal Philadelphia Notes published in 1978, Auslander
introduced the concept of morphisms being determined by modules. Auslander was very …

We introduce and study a new class of morphisms which includes morphisms represented
by monomorphisms in the sense of Auslander and Bridger. As an application, we give not …

We derive a necessary and sufficient condition that an isomorphism between the
endomorphism rings of modules be induced by a semi-linear isomorphism of the modules …

Motivated by the work of Baer [1], Kaplansky gave a proof in 1954 that any isomorphism of
the endomorphism algebras of two torsion modules over a complete discrete valuation …

In [2 1, Fuchs has shown that R is a test module for quasiinjective modules. He showed that
if M is a right R-module, M is quasi-injective if and only if for each right ideal K of R, every R …

Let R be a ring, Let A, C be left R-modules and f: A-+ C an epimorphism. f is called pure if
Hom (M, f): Hom.(M, A)-+ Hom,(M, C) is an epimorphism for all finitely presented left R …

An endomorphism e of a polynomial algebra A [X,,.... X,] is defined by the polynomials e
(Xi)= P,. Such a morphism r is etale when the jacobian of these polynomials is an invertible …

Absolutely pure modules act in ways similar to injective modules. Therefore, through-out this
document we investigate many of these properties of absolutely pure modules which are …

This paper could be regarded as continuation of [7] by AK Gupta and K. Varadarajan.
Throughout this paper we will be following the standard convention in ring theory. The rings …

A new category equivalence is proved in this paper, involving the two distinct categories of
modules, the covariant and the contravariant, respectively, released by Higgins and …