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Monoids with stable torsion-free polygons. (Russian, English) Zbl 1016.20048
Algebra Logika 41, No. 4, 481-492 (2002); translation in Algebra Logic 41, No. 4, 267-273 (2002).
Let \(S\) be a monoid with unity \(1\). An \(S\)-polygon is an algebraic system \(_SA=\langle A,s\rangle_{s\in S}\) with the properties \(s_1(s_2a)=(s_1s_2)a\) and \(1a=a\) for all \(s_1,s_2\in S\), \(a\in A\). A polygon is torsion-free if \(sa=sb\Rightarrow a=b\) for all \(a,b\in A\) and all cancellable \(s\in S\).
The author investigates the model theoretical structure of the class of torsion-free polygons.
20M30 Representation of semigroups; actions of semigroups on sets
03C45 Classification theory, stability, and related concepts in model theory
03C60 Model-theoretic algebra
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