DIVISIBILITY PROPERTIES RELATED TO STAR-OPERATIONS ON INTEGRAL DOMAINS

Year 2012, Volume: 12 Issue: 12, 53 - 74, 01.12.2012

Mi Hee Park Francesca Tartarone

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.

Keywords

GCD, star operation

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• Department of Mathematics Chung-Ang University Seoul 156-756, Korea e-mail: [e-mail] Francesca Tartarone Dipartimento di Matematica Universit`a degli studi Roma Tre Largo San Leonardo Murialdo , 00146 Roma, Italy e-mail: [e-mail]