Semilattices of Nil-extensions of Simple Regular Semigroups

Abstract

Semigroups decomposable into a semilattice of Archimedean semigroups, having certain additional properties such as the intra-, left, right and complete π-regularity, have been investigated in many papers. In the present paper, we study the π-regular ones. Among other things, we characterize them as semilattices of nil-extensions of simple regular semigroups. The obtained results generalize some results given by Munn, Putcha, Shevrin, Bogdanović, Ćirić, and others.

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Correspondence to Stojan Bogdanović.

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2000 Mathematics Subject Classification: 20M10, 20M17

Communicated by K.P. Shum

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Bogdanović, S., Ćirić, M. & Mitrović, M. Semilattices of Nil-extensions of Simple Regular Semigroups. Algebra Colloq. 10, 81–90 (2003). https://doi.org/10.1007/s100110300010

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Keywords:

  • simple semigroups
  • regular semigroups
  • nil-extensions
  • semilattice decompositions