An integral domain R is a GCD-Bezout domain if the Bezout identity holds for any nite 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 dene a (semi)star operation, the q-operation, which is closely related to the w-operation and the p-operation introduced by Anderson in [2]. We use q- to characterize the GCD-Bezout domains and study various properties of these domains.

Park M., H., Tartarone, F. (2012). Divisibility properties related to star-operations on integral domains. INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 12, 53-74.

Divisibility properties related to star-operations on integral domains

TARTARONE, FRANCESCA
2012-01-01

Abstract

An integral domain R is a GCD-Bezout domain if the Bezout identity holds for any nite 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 dene a (semi)star operation, the q-operation, which is closely related to the w-operation and the p-operation introduced by Anderson in [2]. We use q- to characterize the GCD-Bezout domains and study various properties of these domains.
2012
Park M., H., Tartarone, F. (2012). Divisibility properties related to star-operations on integral domains. INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 12, 53-74.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/142151
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