Open Access(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups
Author(s) -
Leila Nouri,
Hossein Mohammadzadeh Saany
Publication year - 2022
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4050
Subject(s) - simple (philosophy) , semigroup , mathematics , special classes of semigroups , krohn–rhodes theory , pure mathematics , discrete mathematics , philosophy , epistemology
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.