(sigma;tau)-Generalized Power Series Over Zip and Weak Zip Rings

Abstract

In this paper we give a new class of extension rings called the (segma;taw)-generalized power
series ring with coecients in a ring R and exponents in a strictly ordered monoid
S which extends Ribenboim's and Ziembowski's constructions of generalized and skew generalized power series rings, respectively. The weak annihilator property of the (segma;taw)-generalized power series ring is investigated in this paper. We also show, under certain conditions, that the (segma;taw)-generalized power series ring is a right zip (weak zip) ring if and only if R is a right zip (weak zip) ring.