Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Semilattice congruences viewed from quasi-orders

Author: Takayuki Tamura
Journal: Proc. Amer. Math. Soc. 41 (1973), 75-79
MSC: Primary 20M10
MathSciNet review: 0333048
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Abstract: Let $ S$ be a semigroup. This paper proves that the smallest semilattice congruence $ {\rho _0}$ containing a compatible binary relation $ \xi $ on $ S$ equals the natural equivalence of the smallest lower-potent positive quasi-order $ {\sigma _0}$ containing $ \xi $.

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Keywords: (Smallest) semilattice congruence, quasi-orders, lower-potent, positive, half-congruences, compatible, natural equivalences, natural quasi-orders, attainability of semilattice
Article copyright: © Copyright 1973 American Mathematical Society