المجلة الدولية للعلوم والتقنية

A ring R is called α-*-skew *-Armendariz*-rings if whenever the polynomials p=∑_(i=0)^m▒〖a_i x^i 〗 and q=∑_(j=0)^n▒a_j x^j ∈ R[x,α] satisfy p(x)q(x) = p(x)q^* (x) = 0, then a_i α^j (b_j )= 0 for all i,j (consequently a_i α^j (b_j^* )= 0 ), which is a proper generalization of reduced*-rings. We study the condition for α-*-skew *-Armendariz*-rings to be reduced. In addition, we discuss many properties of α-*-skew *-Armendariz *-ring. Also, we give the relationship between the Baerness of a *-ring R. Finally, we generalize the property of α-*-skew *-Armendariz to some know extensions. Key Words: *-Armendariz *-rings, *-skew polynomial *-rings, rigid *-rings, *-Baer *-rings.