On nil generalized power serieswise Armendariz rings
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We in this note introduce a concept, so called nil general-ized power serieswise Armendariz ring, that is a generalization of bothS-Armendariz rings and nil power serieswise Armendariz rings. We firstobserve the basic properties of nil generalized power serieswise Armen-dariz rings, constructing typical examples. We next study the relationshipbetween the nilpotent property of R and that of the generalized powerseries ring [[RS,≤]] whenever R is nil generalized power serieswise Armen-dariz.
Abstract
We in this note introduce a concept, so called nil general-ized power serieswise Armendariz ring, that is a generalization of bothS-Armendariz rings and nil power serieswise Armendariz rings. We firstobserve the basic properties of nil generalized power serieswise Armen-dariz rings, constructing typical examples. We next study the relationshipbetween the nilpotent property of R and that of the generalized powerseries ring [[RS,≤]] whenever R is nil generalized power serieswise Armen-dariz.
참고문헌 (16)
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