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Absolute flatness of regular semigroups with a finite height function

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Abstract

In this paper we give a sufficient condition for regular semigroups with a finite height function to be left absolutely flat. As a consequence, we can show that the semigroup Λ(S) of all right translations of a primitive regular semigroupS with only finitely manyR-classes, with composition being from left to right, is absolutely flat and give a generalization of a Bulman-Fleming and McDowell result concerning absolutely flat semigroups from primitive regular semigroups to regular semigroups with a finite height function. These results give examples of semigroups which are amalgamation bases in the class of semigroups.

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Authors and Affiliations

  1. Department of Mathematics, Shimane University Matsue, Shimane, 690, Japan

    K. Shoji

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  1. K. Shoji
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Additional information

Communicated by T. E. Hall

The author thanks the referee for finding errors in the original version of this paper.

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Shoji, K. Absolute flatness of regular semigroups with a finite height function. Semigroup Forum 52, 133–140 (1996). https://doi.org/10.1007/BF02574090

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  • DOI: https://doi.org/10.1007/BF02574090

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