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Semigroups with midunits

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Abstract

A semigroup S has a midunit u if aub=ab for all a and b in S. It is the purpose of this paper to explore semigroups containing midunits and to find an analog to the group of units. The concepts of rectangular group and Bruck-Reilly construction will be extended to produce some semigroups with midunits, and an abstract characterization will be made of certain of these semigroups.

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Authors and Affiliations

  1. Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    Janet E. Ault

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  1. Janet E. Ault
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Communicated by P. A. Grillet

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Ault, J.E. Semigroups with midunits. Semigroup Forum 6, 346–351 (1973). https://doi.org/10.1007/BF02389143

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  • DOI: https://doi.org/10.1007/BF02389143

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