Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 267-275
doi: 10.7151/dmgaa.1089

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David Stanovský

Charles University in Prague,
KA MFF UK, Sokolovská 83,
18675 Praha, Czech Republic

e-mail: stanovsk@karlin.mff.cuni.cz


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.

2000 Mathematics Subject Classification: 08B15, 08B20, 08B26, 20N02.


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Received 13 August 2004
Revised 30 December 2004