J. Jezek, Department of Algebra, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail: jezek@karlin.mff.cuni.cz
Abstract: Idempotent slim groupoids are groupoids satisfying $xxx$ 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.
Keywords: groupoid, variety, nonfinitely based
Classification (MSC 2000): 20N02
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