## Groupoids and the associative law. XII: Representable cardinal functions.(English)Zbl 0904.20049

[For part IX of this series see ibid. 38, No. 1, 39-52 (1997; Zbl 0889.20042).]
In this paper is studied under what conditions is a mapping $$f$$ of a semigroup $$S$$ into the class of cardinals representable by a groupoid $$G$$ and a homomorphism $$g$$ of $$G$$ onto $$S$$ such that $$\ker(g)$$ is the associativity congruence of $$G$$ and $$\text{Card}(g^{-1}(x))=f(x)$$ for every $$x\in S$$.

### MSC:

 20N02 Sets with a single binary operation (groupoids)

### Keywords:

semigroups; groupoids; associativity congruences

Zbl 0889.20042
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