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141.
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
142.
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
143.
144.
Let R be commutative ring with identity and let M be an infinite unitary R-module. Call M homomorphically congruent (HC for short) provided M/N ? M for every submodule N of M for which |M/N| = |M|. In this article, we study HC modules over commutative rings. After a fairly comprehensive review of the literature, several natural examples are presented to motivate our study. We then prove some general results on HC modules, including HC module-theoretic characterizations of discrete valuation rings, almost Dedekind domains, and fields. We also provide a characterization of the HC modules over a Dedekind domain, extending Scott's classification over ? in [22]. Finally, we close with some open questions. 相似文献
145.
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