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Transactions of the American Mathematical Society

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

 
 

 

Extending congruences on semigroups


Author: A. R. Stralka
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
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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.


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Keywords: Topological semigroup, semigroup, congruence, naturally ordered band, <I>N</I>-inversive
Article copyright: © Copyright 1972 American Mathematical Society