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Clifford Regular Domains

✍ Scribed by S Bazzoni

Book ID
102572212
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
138 KB
Volume
238
Category
Article
ISSN
0021-8693

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✦ Synopsis

The class semigroup of a commutative integral domain R is the semigroup S S R of the isomorphism classes of the nonzero ideals of R with operation induced by Ž . multiplication. A domain R is said to be Clifford regular if S S R is a Clifford Ž . semigroup, i.e. S 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.

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## Abstract The main theme of this paper is to construct Clifford analytic‐complete function systems in the generalized Bergman spaces: __B__^__p__^~Cl__n__~(Ω):=ker__D__(Ω)∩__L__^__p__^~Cl__n__~(Ω), and __B__^__p__,2^~Cl__n__~(Ω):=ker▵(Ω)∩__L__^__p__^~Cl__n__~(Ω). These systems are used to approxi