Consider a class C of projective R-modules, where R is a commutative ring with identity,
which satisfies the conditions of (2), namely that C is closed under the operations of direct …

Let R be a left and right Noetherian ring and RωR a faithfully balanced self-orthogonal
bimodule. We introduce the notions of special embeddings and modules of ω-D-class n, and …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

The famous finitistic dimension conjecture says that every finite-dimensional 𝕂-algebra over
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …

Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C⁢(R op)
and ℬ C⁢(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C⁢(R …

Let R be a commutative local Noetherian ring. We prove that the existence of a chain of
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for …

Let $(R,\m) $ be a Noetherian local ring. Consider the notion of homological dimension of a
module, denoted H-dim, for H= Reg, CI, CI $ _* $, G, G $^* $ or CM. We prove that, if for a …

Let R and S be arbitrary associative rings. Given a bimodule, we denote by and the functors
and, where or S. We say that is a finitistic weakly cotilting bimodule (briefly FWC) if for each …

Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …