共查询到19条相似文献,搜索用时 78 毫秒
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In this paper, we characterize the structure of group graded primitive rings having minimal graded one-sided ideals in terms of graded dual modules. We also show that two structure representations of this class of graded primitive rings are both in a sense uniquely determined by the graded primitive rings considered. 相似文献
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设G是任意群,本文给出了G-集G/H-分次模的分次自同态环的刻画.特别地,对我们证得N(H)/H-分次自同态环END(G/H,R)-gr(M)等于分次环ENDR(M)N(H)/H. 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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对任意群G,〔1〕研究了有单位元1的G-分次环与有限可迁G-集的Smash积,在本文中,我们对任意可迁G-集A讨论了具有局部单元元的G-分次环与G-集A的Smash积,证明了有关的一个Mahchke-type定理,推广了〔2〕〔3〕中的一些重要结果。 相似文献
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设R是G-分次环,H是G的子群,本文通过构造两个Moritacontext,给出了环B{H}Morita等价于R_H,R#G ̄*Morita等价于R_H#H ̄*的充分必要条件. 相似文献
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D. J. Benson 《Algebras and Representation Theory》1999,2(3):287-294
Let k be a commutative ring of coefficients and G be a finite group. Does there exist a flat k G-module which is projective as a k-module but not as a k G-module? We relate this question to the question of existence of a k-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have |k| ≥ ?ω. There can be no such example if k is Noetherian of finite Krull dimension, or if k is perfect. 相似文献
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文章对$3\times 3$阶三角矩阵环$$\Gamma = \left(\begin{array}{ccc}T & 0 & 0 \\M & U & 0\\{N \otimes _U M} & N & V \\\end{array}\right)$$上的模作了研究,其中T,U,V均是环, M,N分别是U-T, V-U双模.通过用一个五元组$(A,B,C;f,g)$来描述一个左$\Gamma$-模 (其中$A \in \mod T, B\in {\rm mod} U, C \in {\rm mod} V$, $f:M \otimes _T A \to B \in {\rm mod} U, g:N \otimes _U B \to C \in {\rm mod} V$), 文章分别刻画了$\Gamma$上的一致模、空的模、有限嵌入模,并且确定了${ }_\Gamma (A \oplus B \oplus C)$的根和基座. 相似文献
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E. Alcock 《Journal of Algebra》1999,220(2):1577
We study Kropholler's generalisation of Lazard's criterion for a module to be flat. The context is complete cohomology and modules of type (FP)∞. Let G be a group in the class
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of groups which act on a finite dimensional contractible cell complex with finite stabilisers and let R be a strongly G-graded algebra. We provide a characterisation of the stably flat R-modules under the assumption that R1 is coherent of finite global dimension. 相似文献
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A right module M over a ring R is said to be ADS if for every decomposition M = S ⊕ T and every complement T′ of S, we have M = S ⊕ T′. In this article, we study and provide several new characterizations of this new class of modules. We prove that M is semisimple if and only if every module in σ[M] is ADS. SC and SI rings also characterized by the ADS notion. A ring R is right SC-ring if and only if every 2-generated singular R-module is ADS. 相似文献
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Yueming Xiang 《数学研究通讯:英文版》2013,29(2):121-130
A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R,
K +I≠R$. A ring $R$ is called left $PS$-coherent if every principally small left ideal $Ra$ is finitely presented. We develop, in this paper, $PS$-coherent rings as a generalization
of $P$-coherent rings and $J$-coherent rings. To characterize $PS$-coherent rings, we first
introduce $PS$-injective and $PS$-flat modules, and discuss the relation between them
over some spacial rings. Some properties of left $PS$-coherent rings are also studied. 相似文献