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 …

In this paper, for a fixed semidualizing module C, we introduce the notion of DC-projective
modules which are the special setting of GC-projective modules introduced by White [D …

Given modules M and P, we introduce in section 2 the concept of an (M, P)-injective module.
This concept contains many versions of injectivity known in the literature, such as principal …

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 …

Given modules M and A, M is said to be A-RD-subinjective if for every RD-extension B of A,
every f∈ Hom (A, M) extends to Hom (B, M). For a module M, the RD-subinjectivity domain …

Through concepts from non-commutative algebra and homology, this paper resolves the
conjecture that lets the first bifunctor extension to be zero when the projective dimension is …

In this paper we study modules with the WFI+-extending property. We prove that if M satisfies
the WFI+-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then …

Given modules X and Y, X is said to be Y-subprojective if for every epimorphism\(\pi:
P\rightarrow Y\) and every homomorphism\(\alpha: X\rightarrow Y\), there exists a …

Weak-injective modules were defined as modules M for which E xt R 1 (N, M)= 0 holds for all
modules N of weak dimension≤ 1. They were studied over integral domains in several …

In this paper, we explore the relation between small cofinite irreducibles and cyclic
submodules in the dual. As an application, we show that an Artinian module over a …