Abstract: For a ring endomorphismα,in this paper we introduce the notion of α-power-serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α-power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.

Key words: nil-Armendariz rings, skew power series ring, nilpotent elements