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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
DOI: https://doi.org/10.1090/S0002-9939-1987-0870772-4
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$.

References [Enhancements On Off] (What's this?)

  • [1] Gérard Lallement, Semigroups and combinatorial applications, John Wiley & Sons, New York-Chichester-Brisbane, 1979. Pure and Applied Mathematics; A Wiley-Interscience Publication. MR 530552
  • [2] Mario Petrich, Inverse semigroups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 752899

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0870772-4
Keywords: Perfect congruence, free monoid, $ \vee $-isomorphism
Article copyright: © Copyright 1987 American Mathematical Society