Geodesic
Varieties of idempotent slim groupoids
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1289-1309 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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},
     year = {2007},
     volume = {57},
     number = {4},
     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/