Perfect congruences on a free monoid
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- by Mario Petrich and C. M. Reis
- Proc. Amer. Math. Soc. 99 (1987), 205-212
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870772-4
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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
- 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
Bibliographic 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