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Compatible tolerances on groupoids. (English) Zbl 0768.20027

A compatible tolerance on a groupoid \((G,\cdot)\) is a reflexive and symmetric binary relation which is a subalgebra of \(G \times G\). If all compatible tolerances on \(G\) are congruences, then \(G\) is called tolerance-trivial. In the paper conditions for groupoids to be tolerance- trivial are studied. In the first paragraph these conditions are expressed by means of the covering of groupoids by left or right ideals, in the second paragraph by means of bilateral ideals. The third paragraph studies the classes of tolerance-trivial groupoids. The fourth paragraph is devoted to strongly tolerance-trivial groupoids, i. e. groupoids all whose subgroupoids are tolerance-trivial.

MSC:

20M10 General structure theory for semigroups
08A30 Subalgebras, congruence relations
20M15 Mappings of semigroups
20N02 Sets with a single binary operation (groupoids)
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References:

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