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.
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机译：我们在本说明中介绍了一个概念，即所谓的nil广义幂级数的Armendariz环，即$ S $ -Armendariz环和nil幂级数的Armendariz环的广义。我们首先观察nil广义幂级数Armendariz环的基本性质，并构建典型示例。接下来，我们将研究$ R $的幂等性质与广义幂级数环$ [[[R ^ {S， leq}]] $的关系，只要$ R $是零广义幂级数Armendariz。
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