ORE EXTENSIONS OF WEAK ZIP RINGS∗

摘要

In this paper we introduce the notion of weak zip rings and investigatentheir properties. We mainly prove that a ring R is right (left) weak zip if and only ifnfor any n, the n-by-n upper triangular matrix ring Tn(R) is right (left) weak zip. Let αnbe an endomorphism and δ an α-derivation of a ring R. Then R is a right (left) weaknzip ring if and only if the skew polynomial ring R[x; α, δ] is a right (left) weak zip ringnwhen R is (α, δ)-compatible and reversible.