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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Semigroups over trees
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by M. W. Mislove
Trans. Amer. Math. Soc. 195 (1974), 383-400
DOI: https://doi.org/10.1090/S0002-9947-1974-0352321-8

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.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 195 (1974), 383-400
  • MSC: Primary 22A15
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0352321-8
  • MathSciNet review: 0352321