On varieties of left distributive left idempotent groupoids

• Autorzy: David Stanovský
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

left distributivity; left idempotence; right zero band; LDLI groupoids; subdirectly irreducible; free groupoid; lattice of subvarieties

Kategorie tematyczne

• 20N02: Sets with a single binary operation (groupoids)
• 08B20: Free algebras
• 08B15: Lattices of varieties
• 08B26: Subdirect products and subdirect irreducibility

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2004
• Tom: 24
• Numer: 2
• Strony: 267-275

Daty

wydano

2004

otrzymano

2004-08-13

poprawiono

2004-12-30

Twórcy

autor

David Stanovský

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

Bibliografia

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• [4] P. Jedlicka, On left distributive left idempotent groupoids, Comment. Math. Univ. Carolinae, to appear.
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• [6] J. Płonka, On k-cyclic groupoids, Math. Japon. 30 (1985), 371-382.
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• [8] H. Ryder, The congruence structure of racks, Comm. Algebra 23 (1995), 4971-4989.
• [9] D. Stanovský, Left distributive left quasigroups, PhD Thesis, Charles University in Prague, 2004, Available at http://www.karlin.mff.cuni.cz/~stanovsk/math/disert.pdf.

Identyfikatory

DOI

10.7151/dmgaa.1089