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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Perfect congruences on a free monoid


Authors: Mario Petrich and C. M. Reis
Journal: Proc. Amer. Math. Soc. 99 (1987), 205-212
MSC: Primary 20M10; Secondary 20M15
MathSciNet review: 870772
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Abstract: Perfect congruences on a free monoid $ {X^*}$ are characterized in terms of congruences generated by partitions of $ X \cup \{ 1\} $. It is established that the upper semilattice of perfect congruences if $ \vee $-isomorphic to the upper semi-lattice of partitions on $ X \cup \{ 1\} $. A sublattice of the upper semilattice of perfect congruences is proved to be lattice isomorphic to the lattice of partitions on $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870772-4
PII: S 0002-9939(1987)0870772-4
Keywords: Perfect congruence, free monoid, $ \vee $-isomorphism
Article copyright: © Copyright 1987 American Mathematical Society