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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Extending congruences on semigroups
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by A. R. Stralka
Trans. Amer. Math. Soc. 166 (1972), 147-161
DOI: https://doi.org/10.1090/S0002-9947-1972-0294557-9

Abstract:

The two main results are: (1) Let S be a semigroup which satisfies the relation $abcd = acbd$, let A be a subsemigroup of Reg S which is a band of groups and let $[\varphi ]$ be a congruence on A. Then $[\varphi ]$ can be extended to a congruence on S. (2) Let S be a compact topological semigroup which satisfies the relation $abcd = acbd$, let A be a closed subsemigroup of Reg S and let $[\varphi ]$ be a closed congruence on A such that $\dim \varphi (A)|\mathcal {H} = 0$. Then $[\varphi ]$ can be extended to a closed congruence on S.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 166 (1972), 147-161
  • MSC: Primary 22A15
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0294557-9
  • MathSciNet review: 0294557