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Transactions of the American Mathematical Society

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

 

 

The existence of $ {\rm Irr}(X)$


Author: M. W. Mislove
Journal: Trans. Amer. Math. Soc. 175 (1973), 123-140
MSC: Primary 22A15
DOI: https://doi.org/10.1090/S0002-9947-1973-0325839-0
MathSciNet review: 0325839
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Abstract: If X is a compact totally ordered space, we obtain the existence of an irreducible semigroup with idempotents X, $ {\text{Irr}}(X)$, with the property that any irreducible semigroup with idempotents X is the idempotent separating surmorphic image of $ {\text{Irr}}(X)$. Furthermore, it is shown that the Clifford-Miller endomorphism on $ {\text{Irr}}(X)$ is an injection when restricted to each $ \mathcal{H}$-class of $ {\text{Irr}}(X)$. A construction technique for noncompact semigroups is given, and some results about the structure of such semigroups are obtained.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0325839-0
Keywords: Compact semigroup, irreducible semigroup, linked semigroup, $ \mathcal{H}$-linked semigroup, generalized hormos, $ {\text{Irr}}(X)$, Clifford-Miller endomorphism
Article copyright: © Copyright 1973 American Mathematical Society