环R{D,C}的Armendariz性质

The Armendariz property of the ring R{D,C}

研究了一类新的环R{D,C}的Armendariz性质,证明了:(1)环S=R{D,C}是α-Armendariz环,当且仅当D是α-Armendariz环;(2)S=R{D,C}是feckly Armendariz环,当且仅当D是feckly Armendariz环,C/J(D)∩J(C)是Armendariz环.

This paper mainly studies the Armendariz property of a new class of rings R{D,C}.It is proved that:(1)S=R{D,C}is anα-Armendariz ring if and only if Dis anα-Armendariz ring;(2)R[D,C]is a feckly Armendariz ring if and only if D is a feckly Armendariz ring and C/J(D)∩J(C)is Armendariz ring.