MAL'CEV–NEUMANN SERIES OVER ZIP AND WEAK ZIP RINGS

In this paper we show that: if G is a totally ordered group and R is a G-Armendariz ring (an NI ring with nil (R) is nilpotent), then the ring Λ = R((G; σ; τ)) of Mal'cev–Neumann series is a right zip (weak zip) ring if and only if R is.

ORE EXTENSIONS OF WEAK ZIP RINGS

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