| 有限偏序集的分步上同调模 |
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| 引用本文： | 沃军杰,宋传宁,周才军. 有限偏序集的分步上同调模[J]. 上海师范大学学报(自然科学版), 2009, 38(2) |
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| 作者姓名： | 沃军杰 宋传宁 周才军 |
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| 作者单位： | 上海师范大学,数理学院,上海,200234 |
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| 基金项目： | 上海师范大学线性代数精品课程建设项目 |
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| 摘 要： | 主要研究有限偏序集的二重分步上同调模,讨论该类模的一些性质.举例证明该类模不仅与偏序集的拓扑性质有关,而且与其的组合性质有关.并得到如下两个结果:(i)设P是有限偏序集,x1,x2为P中任意的两个元素,d2为P中所有除x1和x2外的其余元素之和.若茗x1,x2之间满足x1x2=O,那么P是零调的当且仅当Hx1+x2Hd2(P)=0.(ii)当P是锥型偏序集,设P1,P2为P的两个互不相交的子集,P=P1∪P2,设d1分别等于P1,P2的所有元素之和,那么Hd1Hd2(P)=O.
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| 关 键 词： | 有限偏序集 二重分步上同调模 零调 锥 |
Steply cohomology modules of finite partially ordered sets |
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| WO Jun-jie,SONG Chuan-ning,ZHOU Cai-jun. Steply cohomology modules of finite partially ordered sets[J]. Journal of Shanghai Normal University(Natural Sciences), 2009, 38(2) |
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| Authors: | WO Jun-jie SONG Chuan-ning ZHOU Cai-jun |
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| Affiliation: | Mathematics and Science College;Shanghai Normal University;Shanghai 200234;China |
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| Abstract: | This paper mainly studies the twice-steply cohomology modules of finite partially ordered sets.Some properties of these modules are discussed.Two examples are given which show that the properties of such modules depend not only on the topological properties,but also on the combinatorial properties of the partially ordered sets.Two results are obtained on follows:(i) Let P be a finite partially ordered set,let x1,x2 be any two elements of P,and d2 be the sum of all the elements except x1,x2 in P,if x1 x2=0,t... |
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| Keywords: | finite partially ordered sets twice-steply cohomology modules cyclic cone |
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