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Generalized power series over zip and weak zip rings. (English) Zbl 1289.16086

Summary: We show that, if \(R\) is a generalized Armendariz (semicommutative right Noetherian) ring and \(S\) is a strictly (strictly totally) ordered monoid, then the generalized power series ring \(\Lambda=[[R^{S,\leq}]]\) is a right zip (weak zip) ring if and only if \(R\) is.

MSC:

16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16S36 Ordinary and skew polynomial rings and semigroup rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16D25 Ideals in associative algebras
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