Logo image
Some remarks on star operations and the class group
Journal article   Open access   Peer reviewed

Some remarks on star operations and the class group

D. D Anderson and David F Anderson
Journal of pure and applied algebra, Vol.51(1-2), pp.27-33
1988
DOI: 10.1016/0022-4049(88)90075-8
url
https://doi.org/10.1016/0022-4049(88)90075-8View
Published (Version of record) Open Access

Abstract

Let D be an integral domain. In the first section we prove two theorems about star operations. In the second section we investigate when the condition I f is principal, for I a divisorial ideal of D and f a nonzero principal prime of D , implies that I is principal. Our main result is that for any integral domain D and multiplicatively closed subset S of D generated by nonzero principal primes, the natural homomorphisms Pic( D )→Pic( D s ) and Cl t ( D )→Cl t ( D s ) are each injective. We give examples to show that these maps need not be surjective.

Details

Metrics

Logo image