On varieties of left distributive left idempotent groupoids
David Stanovský
Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004), p. 267-275 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:287714 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1089,
     author = {David Stanovsk\'y},
     title = {On varieties of left distributive left idempotent groupoids},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {24},
     year = {2004},
     pages = {267-275},
     zbl = {1076.08004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1089}
}

David Stanovský. On varieties of left distributive left idempotent groupoids. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 267-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1089/

[000] [1] G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1935), 433-454. | Zbl 0013.00105

[001] [2] S. Burris and H.P. Sankappanavar, A course in universal algebra, Springer, New York 1981 (and also the (electronic) Millennium Edition 1999). | Zbl 0478.08001

[002] [3] R. Fenn and C. Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992), 343-406. | Zbl 0787.57003

[003] [4] P. Jedlicka, On left distributive left idempotent groupoids, Comment. Math. Univ. Carolinae, to appear. | Zbl 1106.20049

[004] [5] T. Kepka, Non-idempotent left symmetric left distributive groupoids, Comment. Math. Univ. Carolinae 35 (1994), 181-186. | Zbl 0807.20057

[005] [6] J. Płonka, On k-cyclic groupoids, Math. Japon. 30 (1985), 371-382. | Zbl 0572.08004

[006] [7] B. Roszkowska, The lattice of varieties of symmetric idempotent entropic groupoids, Demonstratio Math. 20 (1987), 259-275. | Zbl 0663.20065

[007] [8] H. Ryder, The congruence structure of racks, Comm. Algebra 23 (1995), 4971-4989. | Zbl 0842.57011

[008] [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. | Zbl 1076.08004