中文摘要：

通过引入相对于子环的Armendariz环,研究这样的最小子环ρ,并讨论多项式环的相对Armendariz性质.证明了ρ是理想,且若ρ是半素的Armendariz环,则R是Armendariz环.

英文摘要：

We introduced Armendariz rings relative to a subring and studied such minimum subringρand discussed the relative Armendariz properties of polynomial rings.Furthermore,it is shown thatρis an ideal in a ring Rand ifρis a semiprime Armendariz ring,then Ris an Armendariz ring.