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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Perfect congruences on a free monoid
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by Mario Petrich and C. M. Reis PDF
Proc. Amer. Math. Soc. 99 (1987), 205-212 Request permission

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
  • Gérard Lallement, Semigroups and combinatorial applications, Pure and Applied Mathematics, John Wiley & Sons, New York-Chichester-Brisbane, 1979. MR 530552
  • 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
  • © Copyright 1987 American Mathematical Society
  • 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