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61.
62.
In this paper we give a complete analytic classification of Artin Gorenstein almost stretched algebras, i.e., Artin Gorenstein algebras with Hilbert function {1, n, 2,…, 2, 1,…, 1}. 相似文献
63.
In this article, some new characterizations of Gorenstein projective, injective, and flat modules over commutative noetherian local rings are given. 相似文献
64.
We give a construction for Gorenstein ideals of codimension 4 which we believe have maximal graded Betti numbers for their Hilbert function. 相似文献
65.
Huang Zhaoyong 《代数通讯》2013,41(12):5791-5812
Let λ be an artin algebra and λω λ a faithfully balanced self-orthogonal bimodule. We generalize the notion of the Auslander-Bridger transpose to that of the transpose with respect to λω λand obtain some properties about dual modules with respect toλω λFurther, we characterize cotilting bimodules and give criteria for computing generalized Goren-stein dimension. 相似文献
66.
《代数通讯》2013,41(11):5085-5094
Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-module. The notion grade of M, grade M, has been introduced by Rees as the least integer t ≥ 0 such that Ext t R (M,R) ≠ 0, see [11]. The Gorenstein dimension of M, G-dim M, has been introduced by Auslander as the largest integer t ≥ 0 such that Ext t R (M, R) ≠ 0, see [3]. In this paper the R-module M is called G-perfect if grade M = G-dim M. It is a generalization of perfect module. We prove several results for the new concept similar to the classical results. 相似文献
67.
We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix. 相似文献
68.
Anne-Marie Simon 《代数通讯》2013,41(11):4496-4519
We revisit the notion of q-approximations for a module over a Noetherian ring, originally due to Auslander and Bridger without a name and rediscovered later by Evans and Griffith. We introduce a somewhat symmetric notion of q-hull and provide existence theorems for both q-approximations and q-hulls. The main feature here are existence theorems and characterizations of minimal such ones when the ring is local. The q-hulls being close to the morphism obtained by Auslander and Bridger in their “approximation theorem”, we also obtain for the latter a minimal statement in the case when the ring is local. 相似文献
69.
James E. Arnold 《代数通讯》2013,41(2):599-614
Abstract Let R be a commutative Noetherian local Gorenstein ring with residue field k. We show that G(k), the Gorenstein injective envelope of k, is an artinian R-module, and we compute G(k) in the case where R = k[[S]] is a semigroup ring and S is symmetric. We also show that a certain subring of the endomorphism ring of G(k) is a complete local (but possibly non-commutative) ring. 相似文献
70.