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On zip and weak zip rings of skew generalized power series. (English) Zbl 1272.16042

From the introduction: The motivation of this paper is to continue the study of the transfer of some algebraic properties between the base ring \(R\) and the generalized power series ring \([[R^{S,\leq}]]\), also to extend the results of W. Cortes [Int. J. Math. Math. Sci. 2008, Article ID 496720 (2008; Zbl 1159.16021)], L. Ouyang [Glasg. Math. J. 51, No. 3, 525-537 (2009; Zbl 1186.16017)] and R. M. Salem [Zip and weak zip rings of generalized power series. Southeast Asian Bull. Math. (to appear)] to the skew generalized power series over zip and weak zip rings.

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
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References:

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