DIVISIBILITY PROPERTIES RELATED TO STAR-OPERATIONS ON INTEGRAL DOMAINS

Abstract

An integral domain R is a GCD-Bezout domain if the Bezout identity holds for any finite set of nonzero elements of R whose gcd exists. Such domains are characterized as the DW-domains having the PSP-property. Using the notion of primitive and superprimitive ideals, we define a (semi)star operation, the q-operation, which is closely related to the w-operation and the p-operation introduced by Anderson. We use q-operation to characterize the GCD-Bezout domains and study various properties of these domains.