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Clifford semigroups of ideals in monoids and domains
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Franz Halter-Koch
Published/Copyright:
September 3, 2009
Abstract
We investigate the ideal semigroup and the ideal class semigroup built by the fractional ideals of an ideal system on a monoid or on a domain. We provide criteria for these semigroups to be Clifford semigroups or Boolean semigroups. In particular, we consider the case of valuation monoids (domains) and of Prüfer-like monoids (domains). By the way, we prove that a monoid (domain) is of Krull type if every locally principal ideal is finite.
Received: 2008-01-11
Revised: 2008-03-30
Published Online: 2009-09-03
Published in Print: 2009-November
© de Gruyter 2009
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Articles in the same Issue
- A Hopf theorem for open surfaces in product spaces
- On R. Steinberg's theorem on algebras of coinvariants
- Natural pseudo-distances between closed curves
- Clifford semigroups of ideals in monoids and domains
- Lp norm estimates of eigenfunctions restricted to submanifolds
- Central values of generalized multiple sine functions
- Lp-independence of spectral bounds of non-local Feynman-Kac semigroups
- On pairwise mutually permutable products
- The block structure spaces of real projective spaces and orthogonal calculus of functors II
- Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43–66]
