Geodesic
On varieties of left distributive left idempotent groupoids
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 267-275

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We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.
Keywords: left distributivity, left idempotence, right zero band, LDLI groupoids, subdirectly irreducible, free groupoid, lattice of subvarieties 
Stanovský, David. On varieties of left distributive left idempotent groupoids. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 267-275. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a7/
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