共查询到19条相似文献,搜索用时 46 毫秒
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刘永辉 《纯粹数学与应用数学》1997,13(2):124-128
引入了弱直投射和弱直内射模的概念,给出了它们的一些性质。使用弱直投射和弱直内射模刻划了遗传环、半遗传环、半单环和QF-环。 相似文献
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Zuo Lancui 《大学数学》1998,(1)
本文研究了所有R—投射模都是投射模的环(RP—环),得出了它的几个等价条件,证明了:S=Rn为RP—环当且仅当R为RP—环;∑ni=1Ri为RP—环当且仅当每个Ri为RP—环.讨论了RP—环的左投射维数. 相似文献
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分次环的分次Jacobson根 总被引:25,自引:2,他引:25
本文通过引入弱拟正则元的概念,对一般Monoid分次环A(未必有1)给出以内部元素刻划的分次Jacobson根JG(A).证明当A有1时,JG(A)与通常定义的Jg(A)相等.对JG(A)性质的讨论,推广了最近的许多结果.作为应用,我们给出了Artin分次环的全部基本结构定理. 相似文献
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本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。 相似文献
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群分次环的本原性及分次本原性 总被引:1,自引:0,他引:1
设A是一个用有限群G分次的环,本文给出了Smash积A#G~*为本原环的一个判别准则,并证明了群分次环的每一个本原理想必定包含一个分次本原理想。作为一个推论,得到已被Cohen和Montgomery证实的Bergman猜想的另一个证明。此外还得到了A_1为本原环或单环的判别。 相似文献
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陆仲坚 《纯粹数学与应用数学》2001,17(2):175-179
首先给出了 gr-正则环为分次除环的两个充要条件 ,其次讨论了分次正则环r G(R)和分次 Jacobson根 JG(R)之间的关系 ,最后给出了分次 Abel正则环的结构定理 . 相似文献
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Let R be any ring. A right R-module M is called n-copure projective if Ext1(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext i (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension. 相似文献
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In the paper, we define(inco) project modules of relatively hereditary torsion theory Υ by intersection complement of module and study their properties; secondly, we define the(inco) Υ-semisimple ring by(inco) Υ-projective module and study their properties. When Υ is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a(inco) semisimple ring and satisfies(inco) condition. 相似文献
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Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-injective if Ext d+1 R (P, M) = 0 for any n-presented R-module P. M is said to be (n, d)-projective if Ext1 R (M, N) = 0 for any (n, d)-injective R-module N. We use these concepts to characterize n-coherent rings and (n, d)-rings. Some known results are extended. 相似文献
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M. Jayaraman 《代数通讯》2013,41(11):3331-3345
We study generalizations of regular modules by Ramamurthy and Mabuchi. These are also generalizations of fully right idempotent and fully left idempotent rings, respectively. We also define and study the properties of *-weakly regular modules, a generalization of fully idempotent rings. 相似文献
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This paper investigates the structure of cyclically pure (or C-pure) projective modules. In particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left R-module is pure projective. Also, over a left hereditary Noetherian ring R, a left R-module M is C-pure projective if and only if M = N ⊕ P, where N is a direct sum of cyclic modules and P is a projective left R-module. The relationship C-purity with purity and RD-purity are also studied. It is shown that if R is a local duo-ring, then the C-pure projective left R-modules and the pure projective left R-modules coincide if and only if R is a principal ideal ring. If R is a left perfect duo-ring, then the C-pure projective left R-modules and the pure projective left R-modules coincide if and only if R is left Köthe (i.e., every left R-module is a direct sum of cyclic modules). Also, it is shown that for a ring R, if every C-pure projective left R-module is RD-projective, then R is left Noetherian, every p-injective left R-module is injective and every p-flat right R-module is flat. Finally, it is shown that if R is a left p.p-ring and every C-pure projective left R-module is RD-projective, then R is left Noetherian hereditary. The converse is also true when R is commutative, but it does not hold in the noncommutative case. 相似文献
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Raja Sridharan 《K-Theory》1998,13(3):269-278
Let A be a Noetherian ring of dimension n and P be a projective A module of rank n having trivial determinant. It is proved that if n is even and the image of a generic element g P* is a complete intersection, then [P] = [Q A] in K0(A) for some projective A module Q of rank n – 1. Further, it is proved that if n is odd, A is Cohen–Macaulay and [P] = [Q A] in K0(A) for some projective A module Q of rank n – 1, then P has a unimodular element. 相似文献
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The authors introduce and investigate the Tc-Gorenstein projective, Lc- Gorenstein injective and Hc-Gorenstein flat modules with respect to a semidualizing module C which shares the common properties with the Gorenstein projective, injective and flat modules, respectively. The authors prove that the classes of all the Tc-Gorenstein projective or the Hc-Gorenstein flat modules are exactly those Gorenstein projective or flat modules which are in the Auslander class with respect to C, respectively, and the classes of all the Lc-Gorenstein 'injective modules are exactly those Gorenstein injective modules which are in the Bass class, so the authors get the relations between the Gorenstein projective, injective or flat modules and the C-Gorenstein projective, injective or flat modules. Moreover, the authors consider the Tc(R)-projective and Lc(R)-injective dimensions and Tc(R)-precovers and Lc(R)-preenvelopes. Fiually, the authors study the Hc-Gorenstein flat modules and extend the Foxby equivalences. 相似文献
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文 [1],[2 ]分别研究了Gr NoetherGr 局部 (半局部 )环的同调维数 ,本文主要进一步讨论Gr 凝聚Gr 半局部环的同调性质 .在§ 1中 ,主要刻画交换Gr 凝聚Gr 半局部环R的分次弱整体维数gr.gl.w .dimR ;在§ 2中 ,定义了分次环R的小有限分次投射维数gr.fp .dimR .刻画了gr.fp .dimR =gr .gl.w .dimR的Gr 凝聚环 .由于Gr Noether环是Gr 凝聚的 ,因而本文所得的结果对于Gr Noether环是自然成立的 .同时 ,本文所得的结果 ,也可视为文 [4 ]关于一般交换凝聚环相应结论的推广 . 相似文献