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Transactions of the American Mathematical Society

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Every semigroup is isomorphic to a transitive semigroup of binary relations


Authors: Ralph McKenzie and Boris M. Schein
Journal: Trans. Amer. Math. Soc. 349 (1997), 271-285
MSC (1991): Primary 20M30, 20M10; Secondary 03G15, 04A05, 05C12, 08A02, 20M12, 20M20
DOI: https://doi.org/10.1090/S0002-9947-97-01708-X
MathSciNet review: 1370647
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Abstract: Every (finite) semigroup is isomorphic to a transitive semigroup of binary relations (on a finite set).


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Additional Information

Ralph McKenzie
Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
Email: mckenzie@math.vanderbilt.edu

Boris M. Schein
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: bschein@uafsysb.uark.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01708-X
Keywords: Semigroup of binary relations, labeled multigraph, transitive representation
Received by editor(s): September 20, 1995
Additional Notes: The first author was supported in part by NSF Grant No. DMS–9596043.
Article copyright: © Copyright 1997 American Mathematical Society