Ouyang Lunqun and Liu Jinwang Hunan University of Science and Technology, Huaihua University
Abstract : We in this note introduce a concept, so called nil generalized power serieswise Armendariz ring, that is a generalization of both $S$-Armendariz rings and nil power serieswise Armendariz rings. We first observe the basic properties of nil generalized power serieswise Armendariz rings, constructing typical examples. We next study the relationship between the nilpotent property of $R$ and that of the generalized power series ring $[[R^{S,\leq}]]$ whenever $R$ is nil generalized power serieswise Armendariz.
Keywords : nil generalized power serieswise Armendariz, generalized power series ring, nilpotent property
