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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 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The existence of $\textrm {Irr}(X)$
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by M. W. Mislove PDF
Trans. Amer. Math. Soc. 175 (1973), 123-140 Request permission

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.
References
    F. T. Christoph, Jr., Topological factor semigroups, Notices Amer. Math. Soc. 16 (1969), 328. Abstract #69T-G12.
  • Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
  • Karl Heinrich Hofmann and Paul S. Mostert, Elements of compact semigroups, Charles E. Merrill Books, Inc., Columbus, Ohio, 1966. MR 0209387
  • Robert J. Koch, Threads in compact semigroups, Math. Z. 86 (1964), 312–316. MR 171268, DOI 10.1007/BF01110405
  • L. S. Pontryagin, Topological groups, Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966. Translated from the second Russian edition by Arlen Brown. MR 0201557
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • 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