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121.
Zhixi Wang 《数学学报(英文版)》1995,11(4):435-438
The concern of this paper is to derive formulas for the injective dimension of then- th Weyl algebraA
n
(R) in casek is a field of characteristic zero andR is a commutative affinek-algebra of finite injective dimension. For the casen=1 we prove a more general result from which the above result follows. Such formulas can be viewed as generalizations of the corresponding results given by J. C. McConnell in the caseR has finite global dimension.Project supported in part by the National Natural Science Foundation for Youth 相似文献
122.
Le Thanh Nhan 《代数通讯》2013,41(3):863-878
We introduce a class of modules called generalized f-modules, which contains strictly all f-modules and generalized Cohen–Macaulay modules. The properties of multiplicity, local cohomology modules, localization, completion… of these modules are presented. A result concerning the finiteness of associated primes of local cohomology modules with respect to generalized f-modules is given. Some connections to the coordinate rings of algebraic varieties and Stanley-Reisner rings are considered. 相似文献
123.
Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated. 相似文献
124.
M. Tamer Koşan 《代数通讯》2013,41(2):423-433
Let M be a right R-module and N ∈ σ[M]. A submodule K of N is called δ-M-small if, whenever N = K + X with N/X M-singular, we have N = X. N is called a δ-M-small module if N? K, K is δ-M-small in L for some K, L ∈ σ[M]. In this article, we prove that if M is a finitely generated self-projective generator in σ[M], then M is a Noetherian QF-module if and only if every module in σ[M] is a direct sum of a projective module in σ[M] and a δ-M-small module. As a generalization of a Harada module, a module M is called a δ-Harada module if every injective module in σ[M] is δ M -lifting. Some properties of δ-Harada modules are investigated and a characterization of a Harada module is also obtained. 相似文献
125.
A. A. Tuganbaev 《Mathematical Notes》1999,65(6):739-748
This paper continues the study of Noetherian serial rings. General theorems describing the structure of such rings are proved. In particular, some results concerning π-projective and π-injective modules over serial rings are obtained. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 880–892 June, 1999. 相似文献
126.
Let R be an hereditary Noetherian prime ring (or, HNP-ring, for short), and let S?=?R[x;σ] be a skew polynomial ring over R with σ being an automorphism on R. The aim of the paper is to describe completely the structure of right projective ideals of R[x;σ] where R is an HNP-ring and to obtain that any right projective ideal of S is of the form X𝔟[x;σ], where X is an invertible ideal of S and 𝔟 is a σ-invariant eventually idempotent ideal of R. 相似文献
127.
128.
We first provide an example of a ring such that all possible structural matrix rings over are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix of a structural matrix ring over a semiprime Noetherian ring can be recovered, contrary to the fact that in general cannot be recovered.
129.
130.