Communications of the
Korean Mathematical Society CKMS

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