(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups
Keywords:ideal, (0-) simple semigroups, Completely (0-) simple semigroups, regular semigroup
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.
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.
How to Cite
Copyright (c) 2022 Leila Nouri, Hossein Mohammadzadeh Saany
This work is licensed under a Creative Commons Attribution 4.0 International License.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.