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We extend the definition of a semidualizing module to general associative rings. This
enables us to define and study Auslander and Bass classes with respect to a semidualizing …

Let R be a hereditary, indecomposable, left pure semisimple ring. Inspired by [I. Reiten, CM
Ringel, Infinite dimensional representations of canonical algebras, Canad. J. Math. 58 …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y-
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …

For a ring S, let K 0 (FGFl (S)) and K 0 (FGPr (S)) denote the Grothendieck groups of the
category of all finitely generated flat S-modules and the category of all finitely generated …

An R-module M is said to be an extending module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …

Conditions for the endomorphism ring of a (finitely generated) projective module to be left
(semi) hereditary have been studied in several papers ([2],[7],[8]). In [2] and [8] it is shown …

The representation theory of a ring Δ has been studied by examining the category of
contravariant (additive) functors from the category of finitely generated left Δ-modules to the …

Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …

A well-known result of Small states that if M is a noetherian left R-module having
endomorphism ring S then any nil subring of S is nilpotent. Fisher [4] dualized this result and …