Semigroups over trees

Mislove, M. W.

doi:10.1090/S0002-9947-1974-0352321-8

Semigroups over trees
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Trans. Amer. Math. Soc. 195 (1974), 383-400 Request permission

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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