On root closedness in generalized power series rings

초록

Let A subset of B be commutative rings with unity, let S subset of T be torsion-free cancellative monoids, and let n >= 1. We give a characterization of when the monoid ring A[S] is n-root closed in the monoid ring B[T]. For torsion-free cancellative ordered monoids (S,<=) subset of (T,<=), we also present sufficient conditions and necessary conditions for the generalized power series ring [[A(S,<=)]] to be n-root closed in the generalized power series ring [[B-T,B-<=]].

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