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101.
Helmut Zöschinger 《代数通讯》2013,41(6):1977-1994
Let (R, 𝔪) be a commutative, noetherian, local ring, E the injective hull of the residue field R/𝔪, and M ○○ = Hom R (Hom R (M, E), E) the bidual of an R-module M. We investigate the elements of Ass(M ○○) as well as those of Coatt(M) = {𝔭 ∈ Spec(R)|𝔭 = Ann R (Ann M (𝔭))} and provide criteria for equality in one of the two inclusions Ass(M) ? Ass(M ○○) ? Coatt(M). If R is a Nagata ring and M a minimax module, i.e., an extension of a finitely generated R-module by an artinian R-module, we show that Ass(M ○○) = Ass(M) ∪ {𝔭 ∈ Coatt(M)| R/𝔭 is incomplete}. 相似文献
102.
103.
104.
Naser Zamani 《代数通讯》2013,41(4):1297-1307
Let (R,𝔪) be a local ring and s ≥ ?1. Using the notion of M-sequence in dimension > s, we introduce Cohen–Macaulay modules in dimension > s. Among other things concerning Cohen–Macaulay modules in dimension > s, some finiteness results of the support and the associated primes of local cohomology modules are investigated. 相似文献
105.
Hongbo Zhang 《代数通讯》2013,41(4):1420-1427
An element of a ring R is called “strongly clean” if it is the sum of an idempotent and a unit that commute, and R is called “strongly clean” if every element of R is strongly clean. A module M is called “strongly clean” if its endomorphism ring End(M) is a strongly clean ring. In this article, strongly clean modules are characterized by direct sum decompositions, that is, M is a strongly clean module if and only if whenever M′⊕ B = A 1⊕ A 2 with M′? M, there are decompositions M′ = M 1⊕ M 2, B = B 1⊕ B 2, and A i = C i ⊕ D i (i = 1,2) such that M 1⊕ B 1 = C 1⊕ D 2 = M 1⊕ C 1 and M 2⊕ B 2 = D 1⊕ C 2 = M 2⊕ C 2. 相似文献
106.
Changjian Fu 《代数通讯》2013,41(7):2410-2418
We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi–Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi–Yau triangulated category. This generalizes a recent work of Smith for cluster categories. 相似文献
107.
Xiangyu Feng 《代数通讯》2013,41(5):1700-1708
Let R be a ring and R ω a self-orthogonal module. We introduce the notion of the right orthogonal dimension (relative to R ω) of modules. We give a criterion for computing this relative right orthogonal dimension of modules. For a left coherent and semilocal ring R and a finitely presented self-orthogonal module R ω, we show that the projective dimension of R ω and the right orthogonal dimension (relative to R ω) of R/J are identical, where J is the Jacobson radical of R. As a consequence, we get that R ω has finite projective dimension if and only if every left (finitely presented) R-module has finite right orthogonal dimension (relative to R ω). If ω is a tilting module, we then prove that a left R-module has finite right orthogonal dimension (relative to R ω) if and only if it has a special ω⊥-preenvelope. 相似文献
108.
The aim of this article is to establish, among other results, the asymptotic stability of the depth of the graded pieces of a nonstandard multigraded module. As a corollary, we get the asymptotic stability of the depth of the graded pieces of the multigraded Rees algebra defined by a finite set of ideals and their associated multigraded rings. 相似文献
109.
In this article we first study an equivariant cyclic cohomology for weak H-module agebras over a weak Hopf algebra H with a bijective antipode. Then we define an equivariant K-theory for weak quantum Yetter–Drinfeld algebras over H and establish a generalized Connes' pairing between the equivariant cyclic cohomology and the equivariant K-theory. As an application we consider our theory for groupoids. 相似文献
110.
We prove that all modules over a left GF-closed ring have Gorenstein flat covers. 相似文献