共查询到20条相似文献,搜索用时 15 毫秒
1.
Javad Asadollahi Shokrollah Salarian 《Transactions of the American Mathematical Society》2006,358(5):2183-2203
In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.
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Reza Sazeedeh 《Proceedings of the American Mathematical Society》2004,132(10):2885-2891
In this paper we assume that is a Gorenstein Noetherian ring. We show that if is also a local ring with Krull dimension that is less than or equal to 2, then for any nonzero ideal of , is Gorenstein injective. We establish a relation between Gorenstein injective modules and local cohomology. In fact, we will show that if is a Gorenstein ring, then for any -module its local cohomology modules can be calculated by means of a resolution of by Gorenstein injective modules. Also we prove that if is -Gorenstein, is a Gorenstein injective and is a nonzero ideal of , then is Gorenstein injective.
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Rings with finite Gorenstein injective dimension 总被引:1,自引:0,他引:1
Henrik Holm 《Proceedings of the American Mathematical Society》2004,132(5):1279-1283
In this paper we prove that for any associative ring , and for any left -module with finite projective dimension, the Gorenstein injective dimension equals the usual injective dimension . In particular, if is finite, then also is finite, and thus is Gorenstein (provided that is commutative and Noetherian).
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Selforthogonal modules with finite injective dimension 总被引:3,自引:0,他引:3
HUANG Zhaoyong 《中国科学A辑(英文版)》2000,43(11):1174-1181
The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially
finite. The notion of left orthogonal dimension is introduced, and then a necessary and sufficient condition of selforthogonal
modules having finite injective dimension and a characterization of cotilting modules are given. 相似文献
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《代数通讯》2013,41(11):4415-4432
Abstract Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper, we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. Moreover a characterization of Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings is given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions. 相似文献
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Alina Iacob 《代数通讯》2017,45(5):2238-2244
We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein. 相似文献
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M. Hellus 《Proceedings of the American Mathematical Society》2008,136(7):2313-2321
For a Noetherian ring we call an -module cofinite if there exists an ideal of such that is -cofinite; we show that every cofinite module satisfies . As an application we study the question which local cohomology modules satisfy . There are two situations where the answer is positive. On the other hand, we present two counterexamples, the failure in these two examples coming from different reasons.
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Massoumeh Nikkhah Babaei 《代数通讯》2013,41(11):4635-4643
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 that over a Gorenstein ring any Artinian module possesses a Gorenstein injective envelope which is special and Artinian. 相似文献
10.
Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen–Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts. 相似文献
11.
Ryo Takahashi 《Proceedings of the American Mathematical Society》2007,135(11):3461-3464
In this note, we characterize finite modules locally of finite injective dimension over commutative Noetherian rings in terms of vanishing of Ext modules.
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The main aim of this paper is to obtain a dual result to the now well known Auslander-Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring with residue field k, and M is a non-injective h-divisible Ext-finite R-module of finite Gorenstein injective dimension such that for each i 3 1i \geq 1 Exti (E,M) = 0 for all indecomposable injective R-modules E 1 E(k)E \neq E(k), then the depth of the ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of M. As a consequence, we get that this formula holds over a d-dimensional Gorenstein local ring for every nonzero cosyzygy of a finitely generated R-module and thus in particular each such nth cosyzygy has its Tor-depth equal to the depth of the ring whenever n 3 dn \geq d. 相似文献
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Archiv der Mathematik - The groups having exactly one normalizer are Dedekind groups. All finite groups with exactly two normalizers were classified by Pérez-Ramos in 1988. In this paper we... 相似文献
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令H是有限维Hopf代数,A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广,同时给出A/A^H是Frobenius扩张的条件。 相似文献
19.
Recently, the notion of Gorenstein AC-projective (resp., Gorenstein AC-injective) modules was introduced in [3] by which the so-called “Gorenstein AC-homological algebra” was established. Here, we define and study a notion of Gorenstein AC-projective dimension for complexes (not necessarily bounded) over associative rings, which is inspired by Veliche’s construction of defining Gorenstein projective dimension. In particular, we show that such a dimension can be closely related to the “proper” Gorenstein AC-projective resolutions of complexes induced by a complete and hereditary cotorsion pair in the category of complexes of modules. This enables us to interpret this dimension of a complex in terms of vanishing of the derived functor RHomR(?,?). As applications, some characterizations of the Gorenstein AC-projective dimension of a module are also obtained. 相似文献
20.
Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M with finite Gorenstein dimension is reflexive if and only if M p is reflexive for p ∈ Spec(R) with depth(R p) ? 1, and $G - {\dim _{{R_p}}}$ (M p) ? depth(R p) ? 2 for p ∈ Spec(R) with depth(R p) ? 2. This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n ? 2 we give a characterization of n-Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown that every R-module has a k-torsionless cover provided R is a k-Gorenstein ring. 相似文献