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Perfect elements in Dubreil-Jacotin regular semigroups

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Abstract

IfS is a strong Dubreil-Jacotin regular semigroup thenx∈S is said to beperfect ifx=x(ξ∶x)x where ζ is the bimaximum element ofS. It is shown that the setP(S) of perfect elements is an ideal ofS, and is also a strong Dubreil-Jacotin subsemigroup. It is then proved that every element ofS is perfect if and only ifS is naturally ordered. Finally, necessary and sufficient conditions forP(S) to be orthodox are determined.

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References

  1. Blyth, T. S. and M. F. Janowitz,Residuation Theory, Pergamon Press, 1972.

  2. Blyth, T. S.,Perfect Dubreil-Jacotin semigroups, Proc. Roy. Soc. Edinburgh78A (1977), 101–104.

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  3. Blyth, T. S. and D. B. McAlister,Split orthodox semigroups, Journal of Algebra51 (1978), 491–525.

    Article  MATH  MathSciNet  Google Scholar 

  4. Blyth, T. S. and R. McFadden,Naturally ordered regular semigroups with a greatest idempotent, Proc. Roy. Soc. Edinburgh91A (1981), 107–122.

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  5. McAlister, D. B.,Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups, J. Australian Math. Soc.31 (1981), 325–336.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, University of St. Andrews, Scotland

    T. S. Blyth & Emília Giraldes

  2. Departamento de Matemática, Universidade Nova de Lisboa, Portugal

    T. S. Blyth & Emília Giraldes

Authors
  1. T. S. Blyth
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  2. Emília Giraldes
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Additional information

Communicated by R. McFadden

Support from the Junta Nacional de Investigação Científica e Tecnológica of Portugal is gratefully acknowledged.

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Blyth, T.S., Giraldes, E. Perfect elements in Dubreil-Jacotin regular semigroups. Semigroup Forum 45, 55–62 (1992). https://doi.org/10.1007/BF03025749

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  • DOI: https://doi.org/10.1007/BF03025749

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