Varieties of idempotent slim groupoids
Jaroslav Ježek · Czechoslovak Mathematical Journal · 2007
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.