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Guo, Jun Ying; Guo, Xiao Jiang; Ding, Juan Ying

Free completely \(\mathcal J^{(\ell)}\)-simple semigroups. (English) Zbl 1319.20046

Acta Math. Sin., Engl. Ser. 31, No. 7, 1086-1096 (2015).
Summary: A semigroup is called completely \(\mathcal J^{(\ell)}\)-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely \(\mathcal J^{(\ell)}\)-simple semigroups form a quasivariety. Moreover, the construction of free completely \(\mathcal J^{(\ell)}\)-simple semigroups is given. It is found that a free completely \(\mathcal J^{(\ell)}\)-simple semigroup is just a free completely \(\mathcal J^*\)-simple semigroup and also a full subsemigroup of some completely simple semigroups.

MSC:

20M10 General structure theory for semigroups
20M05 Free semigroups, generators and relations, word problems
20M07 Varieties and pseudovarieties of semigroups

Keywords:

strongly rpp semigroups; free semigroups; completely simple semigroups; Rees matrix semigroups; quasivarieties of semigroups
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References:

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