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 | References | Similar Articles | Additional Information
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 $X$.
- Gérard Lallement, Semigroups and combinatorial applications, John Wiley & Sons, New York-Chichester-Brisbane, 1979. Pure and Applied Mathematics; A Wiley-Interscience Publication. 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
Keywords:
Perfect congruence,
free monoid,
<IMG WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\vee$">-isomorphism
Article copyright:
© Copyright 1987
American Mathematical Society
