(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups
DOI:
https://doi.org/10.22199/issn.0717-6279-4050Keywords:
ideal, (0-) simple semigroups, Completely (0-) simple semigroups, regular semigroupAbstract
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.
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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Copyright (c) 2022 Leila Nouri, Hossein Mohammadzadeh Saany
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