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Hochschild cohomology of truncated quiver algebras

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Science China Mathematics 2007年第5期50卷 727-736页

作者： Yun-ge XU Yang HAN Wen-feng JIANG Faculty of Mathematics&Computer Science Hubei UniversityWuhan 430062China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080China

For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its... 详细信息

关键词： truncated quiver algebra Hochschild cohomology global dimension oriented cycle 16e40 16e10 16G10

Global dimension and left derived functors of Hom

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Science China Mathematics 2007年第6期50卷 887-898页

作者： Li-xin MAO & Nan-qing DING Institute of Mathematics, Nanjing Institute of Technology, Nanjing 211167, China Department of Mathematics, Nanjing University, Nanjing 210093, China Institute of Mathematics Nanjing Institute of Technology Nanjing China Department of Mathematics Nanjing University Nanjing China

It is well known that the right global dimension of a ring R is usually computed by the right derived functors of Hom and the left projective resolutions of right R-modules. In this paper, for a left coherent and right perfect ring R, we characterize the right global dimension of R, from another point of view, using the left derived functors of Hom and the right projective resolutions of right R-modules. It is shown that rD(R) ? n (n ? 2) if and only if the gl right Proj-dim M R ? n?2 if and only if ext n?1(N,M) = 0 for all right R-modules N and M if and only if every (n?2)th Projcosyzygy of a right R-module has a projective envelope with the unique mapping property. It is also proved that rD(R) ? n (n ? 1) if and only if every (n?1)th Proj-cosyzygy of a right R-module has an epic projective envelope if and only if every nth Proj-cosyzygy of a right R-module is projective. As corollaries, the right hereditary rings and the rings R with rD(R) ? 2 are characterized.

关键词： global dimension projective resolution envelope 16e10 16e30 16e05

Gorenstein flatness and injectivity over Gorenstein rings

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Science China Mathematics 2008年第2期51卷 215-218页

作者： SONG WeiLing HUANG ZhaoYong Department of Mathematics Nanjing UniversityNanjing 210093China

Let R be a Gorenstein *** prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are *** addition,we prove that if R→S is a homomorphism of rings and Se is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of e as a left R-module are *** also give some applications of these results.

关键词： Gorenstein flat Gorenstein injective Gorenstein rings 16e10 16e30

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二元广义外代数的循环同调群

科技资讯 2010年第4期8卷 207-207,209页

作者：杨贵诚湖北工业大学商贸学院湖北武汉430079

设Aq=k/(x2,xy+qyx,y2)是含有两个变量的广义外代数,其中q∈k\{0}。基于徐运阁等人对该代数各阶Hochschild同调群的维数清晰地计算,本文在基域的特征为零时,计算了Aq的所有各阶循环同调群的维数。

关键词：二元广义外代数 Hochschild同调群循环同调群 MR(2000)主题分类 16e40 16e10 16G10