This thesis is comprised of three chapters. The first chapter deals with bounded complexes
of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative …

Let $ R $ be a commutative noetherian ring. In this paper, we study specialization-closed
subsets of $\mathrm {Spec} R $. More precisely, we first characterize the specialization …

Let R be a commutative Noetherian ring, Φ a system of ideals of R, a∈ Φ, M an arbitrary R-
module and ta non-negative integer. Let S be a Melkersson subcategory of R-modules …

Let R be a commutative noetherian ring, and 𝒵 a stable under specialization subset of Spec
(R). We introduce a notion of 𝒵-cofiniteness and study its main properties. In the case dim …

Two distinguished types of semidualizing complexes are the shifts of the underlying rings
and dualizing complexes. Let C be a semidualizing complex for an analytically irreducible …

Let R be a commutative Noetherian ring, Z be a stable under specialization subset of Spec
R. It is introduced in, the concept of Z-cofiniteness of an R-complex X∈ D (R). Also it is …

Let (R, m) be a local ring such that the going-up theorem holds for the extension R⊆ R ̂, I
an ideal of R and X∈ D□ f (R), X≃ 0 such that HI c (X) is Artinian I-cofinite, where cd (I, X) …

Let (R, 𝔪) be a local ring, 𝒵 a specialization closed subset of Spec R and X an R-complex
with finitely generated homology and finite dimension. We show that Att RH 𝒵 dim⁡ X …

Let R be a commutative Noetherian ring and ZZ be a subset of Spec R that is stable under
specialization. In the present paper, for all complexes X in D _\sqsubset^ f (R) D⊏ f (R), we …

This expository article delves into the Greenlees-May Duality Theorem which is widely
thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem …