| 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 |
| 广义Macaulay-Northcott模与Tor-群 |
| Generalized Macaulay-Northcott Modules and Tor-Groups |
| 投稿时间：2007-06-03 修订日期：2008-01-03 |
| DOI：10.3770/j.issn:1000-341X.2009.06.024 |
| 中文关键词: 广义Macaulay-Northcott模 广义幂级数环 Tor-群. |
| 英文关键词:generalized Macaulay-Northcott module ring of generalized power series Tor-group. |
| 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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| 中文摘要: |
| 设$(S, \leq)$是artinian严格全序幺半群, $R$ 是右 noetherian 环.设 $M$是有限生成的右$R$-模, $N$是任意左$R$-模. 用 $[[M^{S, \leq}]]$ 和 $[N^{S, \leq}]$ 分别表示$M$上的广义幂级数模和$N$上的广义Macaulay-Northcott模. 我们证明了存在如下的Abelian 群同构: $$Tor_i^{[[R^{S, \leq}]]}([[M^{S, \leq}]], [N^{S,\leq}])\cong |
| 英文摘要: |
| Let $(S, \leq)$ be a strictly totally ordered monoid which is also artinian, and $R$ a right noetherian ring. Assume that $M$ is a finitely generated right $R$-module and $N$ is a left $R$-module. Denote by $[[M^{S, \leq}]]$ and $[N^{S, \leq}]$ the module of generalized power series over $M$, and the generalized Macaulay-Northcott module over $N$, respectively. Then we show that there exists an isomorphism of Abelian groups: $$\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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