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Keywords:
groupoid; variety; nonfinitely based
groupoid; variety; nonfinitely based
Summary:
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.
References:
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[5] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Volume I. Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644
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