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On lattice-ordered Rees matrix \(\Gamma\)-semigroups. (English) Zbl 1289.06038

Summary: The purpose of this paper is to introduce and give some properties of \(l\)-Rees matrix \(\Gamma\)-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix \(\Gamma\)-semigroups, the structure theorem of \(l\)-congruences lattice of \(l\)-\(\Gamma\)-semigroup \(M=\mu^0(G:I,\wedge,\Gamma_e)\) is given, from which it follows that this \(l\)-congruences lattice is distributive.

MSC:

06F99 Ordered structures
20M99 Semigroups
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