Abstract: The present paper deals with whether quotient rings of Armendariz rings are also Armendariz rings. By means of Gauss Lemma and formal m atrix, it is proved that quotient rings of a unique factorization domain (UFD) w ith respect to its princ ipal ideals are Armendariz rings, and we present a condition for R［x］/ (x²-1) to be an Armendariz ring. Some results on Armendariz rings are extende d to skew Armendariz rings. The paper not only generalizes some results in literature but also provides new examples of Armendariz rings.

Key words: Armendariz ring, reduced ring, skew Armendariz ring, u nique factorization domain