The Tor-Groups of Modules of Generalized Power Series

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,≤]].