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Semigroups over generalized trees

Part of: Connections with other structures, applications Topological and differentiable algebraic systems Semigroups

Published online by Cambridge University Press:  09 April 2009

T. E. Hays
T. E. Hays
Affiliation:
The Ohio State University Newark, OhioU.S.A.
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Abstract

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A semigroup over a generalized tree, denoted by the term ℳL-semigroup, is a compact semigroup S such that Green's relation H is a congruence on S and S/H is an abelian generalized tree with idempotent endpoints and E(S/H) a Lawson semilattice. Each such semigroup is characterized as being constructible from cylindrical subsemigroups of S and the generalized tree S/H in a manner similar to the construction of semigroups over trees and of the hormos. Indeed, semigroups over trees are shown to be particular examples of the construction given herein.

Keywords

compact semigroupgeneralized treesemigroup over a treeLawson semilatticeinverse limit preserving functor.

MSC classification

Secondary: 22A15: Structure of topological semigroups 20M10: General structure theory 54H10: Topological representations of algebraic systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 177 - 188
Copyright
Copyright © Australian Mathematical Society 1978

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