Related papers: A Note On Gorenstein Injective Dimension
Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ be the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules…
Given a two-sided noetherian ring $A$ with a dualizing complex, we show that the big finitistic dimension of $A$ is finite if and only if every bounded below Gorenstein-projective-acyclic cochain complex of Gorenstein-projective $A$-modules…
Let $R \to S$ be a local ring homomorphism and $N$ a finitely generated $S$-module. We prove that if the Gorenstein injective dimension of $N$ over $R$ is finite, then it equals the depth of $R$.
Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension~2 in projective space. In this paper we study points in ${\mathbb P}^3$ and curves in…
The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely generated modules over a Noetherian ring, is studied in the context of finitely presented modules over a coherent ring. A generalization of the…
We present a dimension formula for spaces of vector-valued modular forms of integer weight in case the associated multiplier system has finite image, and discuss the weight distribution of the module generators of holomorphic and cusp…
We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological…
Let $(R,\fm)$ be a local ring and let $C$ be a semidualizing $R$--module. In this paper, we are concerned in $C$--injective and $G_{C}$--injective dimensions of certain local cohomology modules of $R$. Firstly, the injective dimension of…
The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.
Motivated by their impact on homological algebra, the change of rings results have been the subject of several interesting works in Gorenstein homological algebra over Noetherian rings. In this paper, we investigate the change of rings…
We give characterizations of Gorenstein projective, Gorenstein flat and Gorenstein injective modules over the group algebra for large families of infinite groups and show that every weak Gorenstein projective, weak Gorenstein flat and weak…
If $M$ is a nonzero finitely generated module over a commutative Noetherian local ring $R$ such that $M$ has finite injective dimension and finite Gorenstein dimension, then it follows from a result of Holm that $M$ has finite projective…
In this paper, we compare the Gorenstein homological dimension of a ring $R$ and of its trivial ring extension by an module $E$.
Given a left noetherian k-algebra A graded by a group G, an injective object I in the category of G-graded A-modules and a morphism from G to another group G', we provide bounds for the injective dimension of I as a G'-graded A-module. For…
In \cite{SSZ}, the authors proved that an Artin algebra $A$ with infinite global dimension has an indecomposable module with infinite projective and infinite injective dimension, giving a new characterisation of algebras with finite global…
We investigate the relationship between the level of a bounded complex over a commutative ring with respect to the class of Gorenstein projective modules and other invariants of the complex or ring, such as projective dimension, Gorenstein…
For a finitely generated module $ M $ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\rm Hom}_R(M,R)$ and ${\rm Hom}_R(M,M)$ has finite injective dimension. A number of new…
Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope which is special and Artinian. This, in particular, yields…
We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for complexes; we also define a generalized Tate cohomology for…
We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria…