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Construction of medial semigroups. (English) Zbl 0567.20040
Let S be a medial semigroup satisfying the quasiidentity \(xy=uv\Rightarrow xzy=uzv\). Then there exist a commutative semigroup \(T(+)\) and two endomorphisms f,g such that \(S\subseteq T\), \(f^ 2=f\), \(g^ 2=g\), \(fg=gf\) and \(ab=f(a)+g(b)\) for all a,b\(\in S\).
Reviewer: T.Kepka

MSC:
20M10 General structure theory for semigroups
20M15 Mappings of semigroups
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