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Varieties of idempotent slim groupoids

Jaroslav Ježek (2007)

Czechoslovak Mathematical Journal

Idempotent slim groupoids are groupoids satisfying x x x ̄ and x ( y z ) x ̄ z . 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.

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