Characterization and axiomatization of all semigroups whose square is group
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Abstract:
In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup). Finally, several equivalent conditions for a semigroup $S$ with $S^2leq S$ (the square-group property) will be considered.
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Journal title
volume 2 issue 2
pages 1- 8
publication date 2015-11-01
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