Congruences on regular semigroups

Authors:
Francis Pastijn and Mario Petrich

Journal:
Trans. Amer. Math. Soc. **295** (1986), 607-633

MSC:
Primary 20M10; Secondary 08A30, 20M17

DOI:
https://doi.org/10.1090/S0002-9947-1986-0833699-3

MathSciNet review:
833699

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a regular semigroup and let be a congruence relation on . The kernel of , in notation , is the union of the idempotent -classes. The trace of , in notation , is the restriction of to the set of idempotents of . The pair is said to be the congruence pair associated with . Congruence pairs can be characterized abstractly, and it turns out that a congruence is uniquely determined by its associated congruence pair. The triple is said to be the congruence triple associated with . Congruence triples can be characterized abstractly and again a congruence relation is uniquely determined by its associated triple.

The consideration of the parameters which appear in the above-mentioned representations of congruence relations gives insight into the structure of the congruence lattice of . For congruence relations and , put if and only if . Then and are complete congruences on the congruence lattice of and .

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DOI:
https://doi.org/10.1090/S0002-9947-1986-0833699-3

Article copyright:
© Copyright 1986
American Mathematical Society