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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.
##### MSC:
 20M30 Representation of semigroups; actions of semigroups on sets 03C45 Classification theory, stability, and related concepts in model theory 03C60 Model-theoretic algebra
##### Keywords:
torsion-free polygons; monoids; stability
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