相对于子环的 Armendariz 环

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。%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 R and ifρ is a semiprime Armendariz ring,then R is an Armendariz ring.