نتایج جستجو برای: gorenstein injective dimension

تعداد نتایج: 115779  

2009

Introduction. Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a suppleme...

2007
E. ENOCHS S. ESTRADA J. R. GARCÍA ROZAS

In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.

Journal: :Comptes Rendus Mathematique 2021

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings R do we have K(AC)=K(R-Inj)?”. We give an answer to such a question. As applications, obtain new homological approach unifies some well-known conditions Krause’s recollement holds, and example show there exists Gorenstein injective module is not AC-injective. also improve Neeman’s an...

2010
Xiao Jin ZHANG Zhao Yong HUANG

Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost sp...

2013
Jianmin Xing Wei Shao

We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained. Keywords—faithfully balanced se...

Journal: :Publications of The Research Institute for Mathematical Sciences 2023

For a left and right Noetherian ring $R$, we give some equivalent characterizations for $\_RR$ satisfying the Auslander condition in terms of flat (resp. injective) dimensions minimal injective coresolution resolution) $R$-modules. Furthermore, prove that an artin algebra $R$ condition, is Gorenstein if only subcategory consisting finitely generated modules contravariantly finite. As applicatio...

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

Journal: :Kyoto Journal of Mathematics 1998

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