By means of Gauss Lemma and formal matrix, it is proved that quotient rings of a unique factorization domain (UFD) with respect to its principal ideals are Armendariz rings, and we present a condition for R[x]/(x 2-1) to be an Armendariz ring.

• 应用Gauss引理及形式矩阵；证明了惟一分解整环(UFD)关于主理想的商环是Armendariz环；给出了R[x]/(x2-1)为Armendariz环的条件.