The class semigroup of a commutative integral domain R is the semigroup S(R) of the isomorphism classes of the nonzero ideals of R with operation induced by multiplication. A domain Ris said to be Clifford regular if S(R) is a Clifford semigroup, i.e. S(R) is the disjoint union of the subgroups associated to the idempotent elements. In this paper we characterize the noetherian and the integrally closed Clifford regular domains and find some properties of an arbitrary Clifford regular domain.
Clifford regular domains
BAZZONI, SILVANA
2001
Abstract
The class semigroup of a commutative integral domain R is the semigroup S(R) of the isomorphism classes of the nonzero ideals of R with operation induced by multiplication. A domain Ris said to be Clifford regular if S(R) is a Clifford semigroup, i.e. S(R) is the disjoint union of the subgroups associated to the idempotent elements. In this paper we characterize the noetherian and the integrally closed Clifford regular domains and find some properties of an arbitrary Clifford regular domain.File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
