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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