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INTEGRAL DOMAINS WITH A FREE SEMIGROUP OF *-INVERTIBLE INTEGRAL *-IDEALS
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 Title & Authors
INTEGRAL DOMAINS WITH A FREE SEMIGROUP OF *-INVERTIBLE INTEGRAL *-IDEALS
Chang, Gyu-Whan; Kim, Hwan-Koo;
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 Abstract
Let * be a star-operation on an integral domain R, and let be the semigroup of *-invertible integral *-ideals of R. In this article, we introduce the concept of a *-coatom, and we then characterize when is a free semigroup with a set of free generators consisting of *-coatoms. In particular, we show that is a free semigroup if and only if R is a Krull domain and each -invertible -ideal is *-invertible. As a corollary, we obtain some characterizations of *-Dedekind domains.
 Keywords
star-operation;free semigroup of *-invertible *-ideals;*-locally factorial Krull domain;-domain;*-Dedekind domain;
 Language
English
 Cited by
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