This paper is motivated by a recent work of C. Faith who has proved that a quotient finite
dimensional module which satisfies the ascending chain condition on subdirectly irreducible …

The classical homological dimensions—the projective, flat, and injective ones—are usually
defined in terms of resolutions and then proved to be computable in terms of vanishing of …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

Let R be a ring and let simp-R be a representative set of all simple (right R-) modules.
Denote by P< ω the class of all modules which are finitely generated and have finite …

Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider
R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R …

This dissertation reviews attempts of dualizing the Goldie dimension. Moreover we choose
one of these attempts as the dualization of Goldie dimension and study modules with this …