(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups

• Nouri, Leila ^[1] ; Mohammadzadeh Saany, Hossein ^[1]
  1. [1] University of Sistan and Baluchestan

     University of Sistan and Baluchestan

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 1, 2022, págs. 83-99
• Idioma: inglés
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• Resumen

  • The structure theorems for (Completely) simple semigroups and (Completely) 0-simple semigroups have proved a powerful tool in the investigation of such semigroups. In this paper, first of all, we define weak simple semigroups and weak 0-simple semigroups and compare them with simple semigroups and 0-simple semigroups respectively.

    Then we give examples of these semigroups and describe the structure of them. Also, we define completely weak simple semigroup and completely weak 0-simple semigroup. Finally, by using Green’s equivalences, we prove some results and give equivalences, for these semigroups.