Generalized Macaulay-Northcott Modules and Tor-Groups
Received:June 03, 2007  Revised:January 03, 2008
Key Words: generalized Macaulay-Northcott module   ring of generalized power series   Tor-group.
Fund Project:the National Natural Science Foundation of China (No.10961021); the Teaching and Research Award Program for Outsanding Young Teachers in Higher Education Institutions of Ministry of Education (No.NCET-02-080).
 Author Name Affiliation LIU Zhong Kui Department of Mathematics, Northwest Normal University, Gansu 730070, China QIAO Hu Sheng Department of Mathematics, Northwest Normal University, Gansu 730070, China
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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: $$\Tor_i^{[[R^{S, \leq}]]}([[M^{S, \leq}]], [N^{S,\leq}])\cong \bigoplus_{s\in S}\Tor_i^R(M, N).$$