The Tor-Groups of Modules of Generalized Power Series

• 来源期刊: 代数集刊(英文版)
• 关键词: module of generalized power series Tor-group strictly ordered monoid
• 年，卷（期）: 2005,（3）
• 页码范围: 477-484
• 页数: 8页
• 语种: 英文

摘要

Let (S, ≤) be a strictly ordered monoid, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N a left R-module. Denote by [[MS,≤]](resp., [[NS,≤]]) the right (resp., left) [[RS,≤]]-module of generalized power series over M (resp., over N). Then we show that there exists an isomorphism of abelian groups Tor[i[RS, ≤]]([[MS,≤]], [[NS,≤]]) ≌ [[(TorRi(M,N))S,≤]].