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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.