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 
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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/