(Completely) weak simple semigroups and (completely) weak 0-simple semigroups. (English) Zbl 1496.20095
Summary: 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.
Keywords:
ideal; (0-)simple semigroups; completely (0-)simple semigroups; regular semigroup; Green’s equivalencesReferences:
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[3] | M. Kilp, U. Knauer and A. Mikhalev, Monoids, Acts and Categorie, Berlin: Walter de Gruyter, 2000 · Zbl 0945.20036 |
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