Let (R,m) be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated R-module. Introduction Throughout this paper, (R,m, k) is a non-trivial commutative Noetherian local ring with unique maximal ideal m and residue field k. Several authors have obtained results on the growth of the sequence of Betti numbers {βn(k)} (...

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen. Most examples satisfy further properties making them what we call semi-complete duality in this paper. We attach relative theory Gorenstein homological algebra to any given pair

Ladders of recollements abelian categories are introduced, and used to address three general problems. a certain height allow construct triangulated categories, involving derived singularity from ones. also tilt recollements, ladders guarantee that properties like Gorenstein projective or injective preserved by some functors in recollements. Breaking symmetry is crucial developing this theory.

LetR be a complete local ring of dimension d over a perfect field of prime characteristic p, and let M be an R-module of finite length and finite projective dimension. S. Dutta showed that the equality limn→∞ `(F n R(M)) pnd = `(M) holds when the ring R is a complete intersection or a Gorenstein ring of dimension at most 3. We construct a module over a Gorenstein ring R of dimension five for wh...

We investigate the relationship between level of a bounded complex over commutative ring with respect to class Gorenstein projective modules and other invariants or ring, such as dimension, Krull dimension. The results build upon work done by J. D. Christensen [7], H. Altmann et al. [1], Avramov [4] for levels finitely generated modules.

We develop a theory of G-dimension over local homomorphisms which encompasses the classical theory of G-dimension for finitely generated modules over local rings. As an application, we prove that a local ring R of characteristic p is Gorenstein if and only if it possesses a nonzero finitely generated module of finite projective dimension that has finite G-dimension when considered as an R-modul...