ArticleOriginal scientific text
Title
On varieties of left distributive left idempotent groupoids
Authors 1
Affiliations
- Charles University in Prague, KA MFF UK, Sokolovská 83, 18675 Praha, Czech Republic
Abstract
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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Pages:
267-275
Main language of publication
English
Received
2004-08-13
Accepted
2004-12-30
Published
2004
DOI: 10.7151/dmgaa.1089
Exact and natural sciences