Geodesic
Varieties of idempotent slim groupoids
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1289-1309.

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Idempotent slim groupoids are groupoids satisfying $xx\=x$ and $x(yz)\=xz$. We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.
Classification : 08B15, 20N02
Keywords: groupoid; variety; nonfinitely based 
@article{CMJ_2007__57_4_a11,
     author = {Je\v{z}ek, J.},
     title = {Varieties of idempotent slim groupoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1289--1309},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2007},
     mrnumber = {2357591},
     zbl = {1161.20056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_4_a11/}
}
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Ježek, J. Varieties of idempotent slim groupoids. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1289-1309. http://geodesic.mathdoc.fr/item/CMJ_2007__57_4_a11/