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Operation inducing systems. (English) Zbl 0636.08002
An operation inducing system is a collection [S,(G,\(\circ),f,h,\Gamma,\cdot]\) composed of a nonempty set S, a groupoid (G,\(\circ)\), functions f:S\(\to G\) and h:S\(\to S\), a subset \(\Gamma\) of G such that f(S)\(\subseteq \Gamma\) and a function “\(\cdot ''\) from \(\Gamma\times S\) into S. The groupoid (S,*) defined by \(x*y=f(x)\cdot h(y)\) is called the induced groupoid. Some earlier constructions used for the description of free commutative medial groupoids and in the representation theory for medial groupoids can be considered as a special type of an operation inducing system. In the present paper conditions on operation inducing systems and the properties engendered by these conditions on induced groupoids are investigated.
Reviewer: J.Ježek

MSC:
08A05 Structure theory of algebraic structures
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
08A40 Operations and polynomials in algebraic structures, primal algebras
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