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 , let *A* be a subsemigroup of Reg *S* which is a band of groups and let be a congruence on *A*. Then can be extended to a congruence on *S*. (2) Let *S* be a compact topological semigroup which satisfies the relation , let *A* be a closed subsemigroup of Reg *S* and let be a closed congruence on *A* such that . Then can be extended to a closed congruence on *S*.

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DOI:
https://doi.org/10.1090/S0002-9947-1972-0294557-9

Keywords:
Topological semigroup,
semigroup,
congruence,
naturally ordered band,
*N*-inversive

Article copyright:
© Copyright 1972
American Mathematical Society