Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1981 · 57 citations · 5 references
Order TheoryTopological SemigroupsRepresentation TheoryRegular Dubreil-jacotin SemigroupsOrdered GroupSemigroup STransformation SemigroupsPartially Ordered SetGroup RepresentationNatural Partial OrderPartial Order
Abstract A partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that { } has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.
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