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Free distributive groupoids. (English) Zbl 0686.20041
Let F be an absolutely free groupoid and E a free monoid of rank 2. If r,s,u,v,w$$\in F$$ are such that $$r=u.vw$$ is a subterm of s and if $$e\in E$$ is its address in s, then $$\bar e(s)$$ is the term obtained from s after replacing r by uv.uw. All these partial transformations $$\bar e,$$ $$e\in E$$, generate a monoid and the main result of the paper is the following: Theorem. Let $$f,g\in S$$. Then $$hf=kg$$ for some $$h,k\in S$$ such that $$dom(hf)=dom(f)\cap dom(g)$$.
Reviewer: T.Kepka

##### MSC:
 20M05 Free semigroups, generators and relations, word problems 08B05 Equational logic, Mal’tsev conditions 20M20 Semigroups of transformations, relations, partitions, etc.
##### Keywords:
free groupoid; free monoid; partial transformations
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##### References:
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