| 广义Macaulay-Northcott模与Tor-群 |
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| 引用本文： | 刘仲奎,乔虎生.广义Macaulay-Northcott模与Tor-群[J].数学研究及应用,2009,29(6):1117-1123. |
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| 作者姓名： | 刘仲奎 乔虎生 |
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| 作者单位： | 西北师范大学数学系, 甘肃 兰州 730070;西北师范大学数学系, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金(No.10961021); 教育部高等学校优秀青年教师教学科研奖励基金(No.NCET-02-080). |
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| 摘 要： | Let （S,≤） be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by MS,≤]] and NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups：Tori RS,≤]]（MS,≤]],NS,≤]）≌ s∈S ToriR （M,N）.
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| 关 键 词： | 广义权 模块 右Noether环 麦 有限生成 群同构 阿贝尔 纳秒 |
| 收稿时间： | 6/3/2007 12:00:00 AM |
| 修稿时间： | 1/3/2008 12:00:00 AM |
Generalized Macaulay-Northcott Modules and Tor-Groups |
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| LIU Zhong Kui and QIAO Hu Sheng.Generalized Macaulay-Northcott Modules and Tor-Groups[J].Journal of Mathematical Research with Applications,2009,29(6):1117-1123. |
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| Authors: | LIU Zhong Kui and QIAO Hu Sheng |
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| Institution: | Department of Mathematics, Northwest Normal University, Gansu 730070, China;Department of Mathematics, Northwest Normal University, Gansu 730070, China |
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| Abstract: | Let $(S, \leq)$ be a strictly totally ordered monoid which is also artinian, and $R$ a right noetherian ring. Assume that $M$ is a finitely generated right $R$-module and $N$ is a left $R$-module. Denote by $M^{S, \leq}]]$ and $N^{S, \leq}]$ the module of generalized power series over $M$, and the generalized Macaulay-Northcott module over $N$, respectively. Then we show that there exists an isomorphism of Abelian groups: $$\Tor_i^{R^{S, \leq}]]}(M^{S, \leq}]], N^{S,\leq}])\cong \bigoplus_{s\in S}\Tor_i^R(M, N).$$ |
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| Keywords: | generalized Macaulay-Northcott module ring of generalized power series Tor-group |
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