On a generalization of central Armendariz rings

In this paper, some properties of -skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central -skew Armendariz rings and investigate their properties. Also, we show that if (e) = e for each idempotent e2 = e 2 R and R is -skew Armendariz, then R is abelian. Moreover, if R is central -skew Armendariz, then R is right p.p-ring if and only if R[x; ] is right p.p-ring. Then it is proved that if t = IR for some positive integer t, R is central -skew Armendariz if and only if the polynomial ring R[x] is central -skew Armendariz if and only if the Laurent polynomial ring R[x; x 􀀀1] is central -skew Armendariz.