On left distributive left idempotent groupoids

Přemysl Jedlička

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 15-20
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Jedlička, Přemysl. "On left distributive left idempotent groupoids." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 15-20. <http://eudml.org/doc/249564>.

@article{Jedlička2005,
abstract = {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.},
author = {Jedlička, Přemysl},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {groupoids; left distributivity; left idempotency; left distributivity; left idempotency},
language = {eng},
number = {1},
pages = {15-20},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On left distributive left idempotent groupoids},
url = {http://eudml.org/doc/249564},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Jedlička, Přemysl
TI - On left distributive left idempotent groupoids
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 15
EP - 20
AB - 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.
LA - eng
KW - groupoids; left distributivity; left idempotency; left distributivity; left idempotency
UR - http://eudml.org/doc/249564
ER -

References

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  1. Dehornoy P., Braids and Self Distributivity, Progress in Mathematics, vol. 192, Birkhäuser, 2000. Zbl0958.20033MR1778150
  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). (1994) Zbl0807.20057MR1292593
  4. Kepka T., Notes on left distributive groupoids, Acta Univ. Carolinae Math. Phys. 22.2 (1981), 23-37. (1981) Zbl0517.20048MR0654379
  5. Kepka T., Němec P., Selfdistributive groupoids, Part A1: Non-idempotent left distributive groupoids, Acta Univ. Carolinae Math. Phys. 44.1 (2003), 3-94. (2003) MR2043197
  6. Stanovský D., Homomorphic images of subdirectly irreducible algebras, Contest Thesis, 2001, http://www.karlin.mff.cuni.cz/~stanovsk/math/publ.htm. 

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