Congruences on regular semigroups
Authors:
Francis Pastijn and Mario Petrich
Journal:
Trans. Amer. Math. Soc. 295 (1986), 607633
MSC:
Primary 20M10; Secondary 08A30, 20M17
MathSciNet review:
833699
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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 abovementioned 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198608336993
PII:
S 00029947(1986)08336993
Article copyright:
© Copyright 1986
American Mathematical Society
