Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
groupoids; left distributivity; left idempotency
groupoids; left distributivity; left idempotency
Summary:
We study the groupoids satisfying both the left distributivity and the left idempotency laws. We show that they possess a canonical congruence admitting an idempotent groupoid as factor. This congruence gives a construction of left idempotent left distributive groupoids from left distributive idempotent groupoids and right constant groupoids.
References:
[1] Dehornoy P.: Braids and Self Distributivity. Progress in Mathematics, vol. 192, Birkhäuser, 2000. MR 1778150 | Zbl 0958.20033
[2] Jedlička P.: Proprieté de treillis pour les groupes de Coxeter et les systèmes LDI. Ph.D. Thesis (in French and Czech), Caen, 2004, 260 pp.
[3] Kepka T.: Non-idempotent left symmetric left distributive groupoids. Comment. Math. Univ. Carolinae 35 1 181-186 (1994). MR 1292593 | Zbl 0807.20057
[4] Kepka T.: Notes on left distributive groupoids. Acta Univ. Carolinae Math. Phys. 22.2 (1981), 23-37. MR 0654379 | Zbl 0517.20048
[5] Kepka T., Němec P.: Selfdistributive groupoids, Part A1: Non-idempotent left distributive groupoids. Acta Univ. Carolinae Math. Phys. 44.1 (2003), 3-94. MR 2043197
[6] Stanovský D.: Homomorphic images of subdirectly irreducible algebras. Contest Thesis, 2001, http://www.karlin.mff.cuni.cz/\char126stanovsk/math/publ.htm
Search
Partner of
