DIVISIBILITY PROPERTIES RELATED TO STAR-OPERATIONS ON INTEGRAL DOMAINS

Authors : Mi Hee PARK, Francesca TARTARONE

Pages : 53-74

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Publication Date : 2012-12-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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.
Keywords : GCD, star operation