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1.
For a commutative noetherian ring R with residue field k stable cohomology modules have been defined for each n∈Z, but their meaning has remained elusive. It is proved that the k-rank of any characterizes important properties of R, such as being regular, complete intersection, or Gorenstein. These numerical characterizations are based on results concerning the structure of Z-graded k-algebra carried by stable cohomology. It is shown that in many cases it is determined by absolute cohomology through a canonical homomorphism of algebras . Some techniques developed in the paper are applicable to the study of stable cohomology functors over general associative rings. 相似文献
2.
Given two positive integers e and s we consider Gorenstein Artinian local rings R whose maximal ideal m satisfies ms≠0=ms+1 and rankR/m(m/m2)=e. We say that R is a compressed Gorenstein local ring when it has maximal length among such rings. It is known that generic Gorenstein Artinian algebras are compressed. If s≠3, we prove that the Poincaré series of all finitely generated modules over a compressed Gorenstein local ring are rational, sharing a common denominator. A formula for the denominator is given. When s is even this formula depends only on the integers e and s . Note that for s=3 examples of compressed Gorenstein local rings with transcendental Poincaré series exist, due to Bøgvad. 相似文献
3.
4.
Reza Sazeedeh 《Journal of Pure and Applied Algebra》2007,211(3):773-783
Let R be a commutative Noetherian ring of Krull dimension d, and let a be an ideal of R. In this paper, we will study the strong cotorsioness and the Gorenstein injectivity of the section functor Γa(−) in local cohomology. As applications, we will find new characterizations for Gorenstein and regular local rings. We also study the effect of the section functors Γa(−) and the functors on the Auslander and Bass classes. 相似文献
5.
Lars Winther Christensen Sean Sather-Wagstaff 《Journal of Pure and Applied Algebra》2010,214(6):982-989
A central problem in the theory of Gorenstein dimensions over commutative noetherian rings is to find resolution-free characterizations of the modules for which these invariants are finite. Over local rings, this problem was recently solved for the Gorenstein flat and the Gorenstein projective dimensions; here we give a solution for the Gorenstein injective dimension. Moreover, we establish two formulas for the Gorenstein injective dimension of modules in terms of the depth invariant; they extend formulas for the injective dimension due to Bass and Chouinard. 相似文献
6.
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an R-module M, we show that M is Gorenstein injective if and only if Hom
R
(Ȓ,M) belongs to Auslander category B(Ȓ), M is cotorsion and Ext
i
R
(E,M) = 0 for all injective R-modules E and all i > 0.
Received: 24 August 2006 Revised: 30 October 2006 相似文献
7.
Kazem Khashyarmanesh 《Archiv der Mathematik》2007,88(5):413-418
Let (
) be a commutative Noetherian local ring with non-zero identity,
an ideal of R and M a finitely generated R-module with
. Let D(–) := Hom
R
(–, E) be the Matlis dual functor, where
is the injective hull of the residue field
. We show that, for a positive integer n, if there exists a regular sequence
and the i-th local cohomology module H
i
a
(M) of M with respect to
is zero for all i with i > n then
The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran
(No. 85130023).
Received: 9 August 2006 相似文献
8.
Naser Zamani 《Archiv der Mathematik》2006,86(4):321-330
Let
be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let
denote the i-th graded generalized local cohomology of N relative to M with support in
. We study the vanishing, tameness and asymptotical stability of the homogeneous components of
.
Received: 22 March 2005; revised: 25 June 2005 相似文献
9.
A semi-dualizing module over a commutative noetherian ring A is a finitely generated module C with RHomA(C,C)?A in the derived category D(A).We show how each such module gives rise to three new homological dimensions which we call C-Gorenstein projective, C-Gorenstein injective, and C-Gorenstein flat dimension, and investigate the properties of these dimensions. 相似文献
10.
Petter Andreas Bergh 《Journal of Pure and Applied Algebra》2008,212(1):262-270
Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology groups assumed to vanish may be arbitrarily far apart from each other. 相似文献
11.
The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find these bounds to be sharp in a wide range of examples. 相似文献
12.
Liana M. ?ega 《Journal of Pure and Applied Algebra》2011,215(6):1263-1269
We prove that the Auslander-Reiten conjecture holds for commutative standard graded artinian algebras, in two situations: the first is under the assumption that the modules considered are graded and generated in a single degree. The second is under the assumption that the algebra is generic Gorenstein of socle degree 3. 相似文献
13.
Sean Sather-Wagstaff 《Journal of Pure and Applied Algebra》2008,212(12):2594-2611
Let R be a local ring and M a finitely generated R-module. The complete intersection dimension of M-defined by Avramov, Gasharov and Peeva, and denoted -is a homological invariant whose finiteness implies that M is similar to a module over a complete intersection. It is related to the classical projective dimension and to Auslander and Bridger’s Gorenstein dimension by the inequalities .Using Blanco and Majadas’ version of complete intersection dimension for local ring homomorphisms, we prove the following generalization of a theorem of Avramov and Foxby: Given local ring homomorphisms φ:R→S and ψ:S→T such that φ has finite Gorenstein dimension, if ψ has finite complete intersection dimension, then the composition ψ°φ has finite Gorenstein dimension. This follows from our result stating that, if M has finite complete intersection dimension, then M is C-reflexive and is in the Auslander class AC(R) for each semidualizing R-complex C. 相似文献
14.
Liana M. Sega 《Proceedings of the American Mathematical Society》2003,131(8):2313-2323
We prove that if , are finite modules over a Gorenstein local ring of codimension at most , then the vanishing of for is equivalent to the vanishing of for . Furthermore, if has no embedded deformation, then such vanishing occurs if and only if or has finite projective dimension.
15.
M. Bakuradze 《Journal of Mathematical Sciences》2013,189(1):10-67
In this paper, we study the interaction between transferred Chern classes and Chern classes of transferred bundles. We calculate the algebra $ B{P^{*}}\left( {X_{{h\varSigma p}}^p} \right) $ and show that its multiplicative structure is completely determined by the Frobenius reciprocity. We also give some tables of the initial segments of the formal group law in the Morava K-theory which are often useful in calculations. 相似文献
16.
Saeed Nasseh Sean Sather-Wagstaff Ryo Takahashi Keller VandeBogert 《Journal of Pure and Applied Algebra》2019,223(3):1272-1287
We construct a local Cohen–Macaulay ring R with a prime ideal such that R satisfies the uniform Auslander condition (UAC), but the localization does not satisfy Auslander's condition (AC). Given any positive integer n, we also construct a local Cohen–Macaulay ring R with a prime ideal such that R has exactly two non-isomorphic semidualizing modules, but the localization has non-isomorphic semidualizing modules. Each of these examples is constructed as a fiber product of two local rings over their common residue field. Additionally, we characterize the non-trivial Cohen–Macaulay fiber products of finite Cohen–Macaulay type. 相似文献
17.
Adela Vraciu 《Mathematische Zeitschrift》2003,244(4):873-885
We study the relationship between the tight closure of an ideal and the sum of all ideals in its linkage class
I thank Mel Hochster and Craig Huneke for their support and encouragement and for many helpful discussions.The author was partially supported by the NSF. 相似文献
18.
Michel van den Bergh 《Proceedings of the American Mathematical Society》1998,126(5):1345-1348
Let ``' stand for Hochschild (co)homology. In this note we show that for many rings there exists such that for an arbitrary -bimodule we have . Such a result may be viewed as an analog of Poincaré duality.
Combining this equality with a computation of Soergel allows one to compute the Hochschild homology of a regular minimal primitive quotient of an enveloping algebra of a semisimple Lie algebra, answering a question of Polo.
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Given a homomorphism of commutative noetherian rings R→S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals , where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension. 相似文献