Perfect congruences on a free monoid
Abstract: Perfect congruences on a free monoid are characterized in terms of congruences generated by partitions of . It is established that the upper semilattice of perfect congruences if -isomorphic to the upper semi-lattice of partitions on . A sublattice of the upper semilattice of perfect congruences is proved to be lattice isomorphic to the lattice of partitions on .
-  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
Keywords: Perfect congruence, free monoid, -isomorphism
Article copyright: © Copyright 1987 American Mathematical Society