On Monogeny and Epigeny Classes of Modules
Received:October 16, 2002  
Key Words: Monogeny class   Epigeny class   generalized power series ring  
Fund Project:Supported by National Natural Science Foundation of China (10171082) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.
Author NameAffiliation
LIU Zhong-kui Dept. of Math.
Northwest Normal University
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      Let (S, ≤) be a strictly totally ordered monoid, and M and N be left R modules. We show the following results: (1) If (S, ≤) is finitely generated and satisfies the condition that 0≤S for any s ∈S, then Epi([[RS,≤]][[MS,≤]]) = Epi([[RS,≤]][[NS,≤]]) if and only if Epi(M) = Epi(N); (2) If (S,≤) is artinian, then Mono([[RS,≤]][MS,≤])= Mono([[RS,≤]][NS,≤]) if and only if Mono(M) = Mono(N).
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