on a generalization of central armendariz rings

In this paper, some properties of α-skew armendariz and central armendariz rings have been studied by variety of others. we generalize the notions to central α-skew armendariz rings and investigate their properties. also, we show that if α(e)=e for each idempotent e^2=e∈r and r is α-skew armendariz, then r is abelian. moreover, if r is central α-skew armendariz, then r is right p.p-ring if and only if r[x;α] is right p.p-ring. then it is proved that if αt=ir for some positive integer t, r is central α-skew armendariz if and only if the polynomial ring r[x] is central α-skew armendariz if and only if the laurent polynomial ring r[x,x^−1] is central α-skew armendariz.‎