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Transactions of the American Mathematical Society
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
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)\vert\mathcal{H} = 0$. Then $ [\varphi ]$ can be extended to a closed congruence on S.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0294557-9
PII: S 0002-9947(1972)0294557-9
Keywords: Topological semigroup, semigroup, congruence, naturally ordered band, N-inversive
Article copyright: © Copyright 1972 American Mathematical Society