By introducing the concept of a power series JArmendariz ring

the study of power series Armendariz rings is further extended. It is shown that: ① let T=〖JB((〗〖HL(2〗R〖〗M0〖〗S〖HL)〗〖JB))〗 be a formal triangular matrix ring. Then T is a power seriesJArmendariz ring if and only if R

S are both power series JArmendariz rings; ② let {Rα〖JB(|〗α∈Λ〖JB)〗} be a family of rings. Then ∏〖DD（X〗α∈Λ〖DD）〗Rα is a power series JArmendariz ring if and only if every Rα is a power series JArmendarizring; ③ if R is a power series JArmendarizring and satisfies J(R)［x］=J(R［x］)

 then R［x］is a power series JArmendariz ring.