Slim groupoids. (English) Zbl 1161.20055

Summary: Slim groupoids are groupoids satisfying \(x(yz)\approx xz\). We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there are just two such groupoids.


20N02 Sets with a single binary operation (groupoids)
08B15 Lattices of varieties
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