Semi Hopfian and Semi Co-Hopfian Modules over Generalized Power Series Rings
نویسنده
چکیده
Let (S,≤) be a strictly totally ordered monoid, R be a commutative ring and M be an R-module. We show the following results: (1) If (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a semi Hopfian [[RS,≤]]-module if and only if M is a semi Hopfian R-module; (2) If (S,≤) is artinian, then the generalized inverse polynomial module [MS,≤] is a semi co-Hopfian [[RS,≤]]-module if and only if M is a semi co-Hopfian R-module. Mathematics Subject Classification: 16W60
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