In this paper, we show that if R is a local Cohen–Macaulay ring admitting a dualizing module
Ω, then Ω-Gorenstein projective and flat covers and Ω-Gorenstein injective envelopes exist …

In this paper, we study injective dimension and Gorenstein injective dimension over local
ring homomorphisms. Some well-known results are generalized. For example, the Bass …

Let R be a commutative Noetherian ring. Let P (R)(respectively, I (R)) be the category of all
finite R-modules of finite projective (respectively, injective) dimension. Sharp [9] constructed …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

Let R be a commutative Noetherian ring and I, J be ideals of R. Let M, N be two R-modules.
For an integer i≥ 0, we define the i-th generalized local cohomology module H< sub> I, J< …

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Let R be a commutative Noetherian ring and aa proper ideal of R. We show that if n:=
gradeR a, then EndR (Hn a (R))∼= Extn R (Hn a (R), R). We also prove that, for a …

Let R=⨁ n≥ 0Rn be a homogeneous Noetherian ring, let M be a finitely generated graded R-
module and let R+=⨁ n> 0Rn. Let b≔ b0+ R+, where b0 is an ideal of R0. In this paper, we …

The concept of Faltings' local-global principle for the minimaxness of local cohomology
modules over a commutative Noetherian ring R is introduced, and it is shown that this …

It is well-known that the ith local cohomology of a finitely generated R-module M over a
positively graded commutative Noetherian ring R, associated to the irrelevant ideal R+ is …