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.
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 
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/
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     title = {Varieties of idempotent slim groupoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1289--1309},
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     volume = {57},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a11/}
}
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