Geodesic
Slim groupoids
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1275-1288 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Slim groupoids are groupoids satisfying $x(yz)\=xz$. 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.
Slim groupoids are groupoids satisfying $x(yz)\=xz$. 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.
Classification : 08B15, 20N02
Keywords: groupoid; variety; nonfinitely based 
@article{CMJ_2007_57_4_a10,
     author = {Je\v{z}ek, J.},
     title = {Slim groupoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1275--1288},
     year = {2007},
     volume = {57},
     number = {4},
     mrnumber = {2357590},
     zbl = {1161.20055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a10/}
}
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Ježek, J. Slim groupoids. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1275-1288. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a10/