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

Authors

  • Leila Nouri University of Sistan and Baluchestan.
  • Hossein Mohammadzadeh Saany University of Sistan and Baluchestan.

DOI:

https://doi.org/10.22199/issn.0717-6279-4050

Keywords:

ideal, (0-) simple semigroups, Completely (0-) simple semigroups, regular semigroup

Abstract

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.

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Author Biographies

  • Leila Nouri, University of Sistan and Baluchestan.

    Department of Mathematics.

  • Hossein Mohammadzadeh Saany, University of Sistan and Baluchestan.

    Department of Mathematics.

References

P. M. Higgins, Techniques of semigroup theory. Oxford: Oxford University, 1992.

J. M. Howie, Fundamentals of semigroup theory. London: Oxford University Press, 1995.

M. Kilp, U. Knauer and A. Mikhalev, Monoids, Acts and Categorie, Berlin: Walter de Gruyter, 2000.

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Published

2022-01-28

Issue

Section

Artículos

How to Cite

[1]
“(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups”, Proyecciones (Antofagasta, On line), vol. 41, no. 1, pp. 83–99, Jan. 2022, doi: 10.22199/issn.0717-6279-4050.