Salem, R. M. Generalized power series over zip and weak zip rings. (English) Zbl 1289.16086 Southeast Asian Bull. Math. 37, No. 2, 259-268 (2013). 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. Cited in 2 Documents 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 Keywords:strictly ordered monoids; generalized power series rings; right zip rings; weak zip rings; Armendariz rings; semicommutative rings PDFBibTeX XMLCite \textit{R. M. Salem}, Southeast Asian Bull. Math. 37, No. 2, 259--268 (2013; Zbl 1289.16086)