共查询到18条相似文献,搜索用时 46 毫秒
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李珍珠 《数学的实践与认识》2004,(4)
引进了分次 wn -模 ,讨论了具有有限分次 FP-自内射维数的 gr凝聚环和分次 wn -模的自反性 .所得的结果推广了 Stentr m,Bass和黄兆泳等人的若干结果 . 相似文献
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弱半局部环的同调性质 总被引:1,自引:0,他引:1
环R称为弱半局部环,如果R/J(R)是Von Neumann正则环.给出了一个交换环是弱半局部环的充分且必要条件;还讨论了交换凝聚弱半局部环及其模的同调维数. 相似文献
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本文推广了环的R-序列的概念,引进了相伴R-序列,讨论了Jacobson根具有AR-性质的Noetherian环的同调维数及其结构性质,推广了交换局部环和半局部环的一些同调性质。 相似文献
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1984年,Ho Kuen Ng在[1]中给出了交换环与模的有限表现维数(简称为F.P.—维数)的定义及若干有意义的重要结果.从此,有限表现性的讨论成为环论的热门课题之一.作者在[2]中将有限表现维数推广到非交换环上.并利用有限表现维数刻划了凝聚环,在[3]中讨论了有限表现维数的换环定理.在[4]中讨论了笛卡尔方形上的有限表现维数.丁南庆在[5]中推广了有限表现维数,给出了一种新维数——模的有限生成维数,在[6]中讨论了有限表现模的对偶 相似文献
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在[1]中,作者讨论了有限整体维数的半局部环上有限生成非零模的同调维数和余维数的和的性质;定义了模N的次全维数(pro-total dimension)ptd_sN、次整体维数(pro-glo-bal dimension) pgd_sN,以及半局部环S本身的全维数 (total dimennsion)tdS;紧接着在§4讨论了上述各种维数之间的关系,然后在§6应用前面的结果去研究tdS=2的半局部环的结构。但我们发现[1]文中的某些结论不成立,本文试图举出[1]文中某些命题不成 相似文献
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设$k$是一个弱维数有限的交换环, $G$是一个群. 本文讨论了群$G$具有有限的Gorenstein同调维数的标准.证明了群$G$的Gorenstein同调维数的有限性与群环$kG$的Gorenstein弱维数的有限性是一致的.进一步,我们给出了Serre定理的一个Gorenstein类比.推广了整环上$G$的Gorenstein同调维数的一些已知结果. 相似文献
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Darin R. Stephenson James J. Zhang 《Proceedings of the American Mathematical Society》1997,125(6):1593-1605
We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using this, we can classify all connected graded noetherian algebras of global dimension two.
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Lucio Centrone 《Linear and Multilinear Algebra》2013,61(12):1433-1450
Let E be the infinite-dimensional Grassmann algebra over a field F of characteristic 0. In this article, we consider the verbally prime algebras M n (F), M n (E) and M a,b (E) endowed with their gradings induced by that of Vasilovsky, and we compute their graded Gelfand--Kirillov dimensions. 相似文献
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Using techniques of localization for Grothendieck categories with a family of projective generators, we show that for a graded
ring R = ⊕
σ∈G
R
σ
with finite support if R
e
has Gabriel dimension then has Gabriel dimension. Moreover, adding some lattice results, we prove that if has Gabriel dimension then also has Gabriel dimension.
This research has been supported by grant MTM2005-3227 from MEC. 相似文献
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Jerzy Dydak 《Transactions of the American Mathematical Society》2006,358(4):1537-1561
The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory, this algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes of graded groups . There are two geometric interpretations of these equivalence classes: 1) For pointed CW complexes and , if and only if the infinite symmetric products and are of the same extension type (i.e., iff for all compact ). 2) For pointed compact spaces and , if and only if and are of the same dimension type (i.e., for all Abelian groups ).
Dranishnikov's version of the Hurewicz Theorem in extension theory becomes for all simply connected .
The concept of cohomological dimension of a pointed compact space with respect to a graded group is introduced. It turns out iff for all . If and are two positive graded groups, then if and only if for all compact .
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Yves Felix Steve Halperin Jean-Claude Thomas 《Proceedings of the American Mathematical Society》2007,135(5):1575-1578
Let be a connected finite type graded Lie algebra. If dim and gldim , then log index . If, moreover, , then for some , dim where log index as
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In this note we show the interlacing between homological algebra and the category of relative Hopf modules. We show that many well-known concepts related with differential graded algebras can be performed as purely Hopf algebraic phenomenons. 相似文献
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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