Abstract:

We introduced Armendariz rings relative to a subring  and studied such minimum subring ρ and discussed the relative Armendariz properties of polynomial rings. Furthermore, it is shown that  ρ is an ideal in a ring R and if ρ is a semiprime Armendariz ring, then R is an Armendariz ring.

Key words:  Armendariz ring, relative Armendariz ring, reduced ring