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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Semigroups over trees


Author: M. W. Mislove
Journal: Trans. Amer. Math. Soc. 195 (1974), 383-400
MSC: Primary 22A15
MathSciNet review: 0352321
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Abstract: A semigroup over a tree is a compact semigroup S such that $ \mathcal{H}$ is a congruence on S and $ S/\mathcal{H}$ is an abelian tree with idempotent endpoints. Each such semigroup is characterized as being constructible from cylindrical subsemigroups of S and the tree $ S/\mathcal{H}$ in a manner similar to the construction of the hormos. Indeed, the hormos is shown to be a particular example of the construction given herein when $ S/\mathcal{H}$ is an I-semigroup. Several results about semigroups whose underlying space is a tree are also established as lemmata for the main results.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0352321-8
Keywords: Compact semigroup, tree, semigroup over a tree, generalized collection, hormos, I-semigroup
Article copyright: © Copyright 1974 American Mathematical Society