| Title:
|
On left distributive left idempotent groupoids (English) |
| Author:
|
Jedlička, Přemysl |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
15-20 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
groupoids |
| Keyword:
|
left distributivity |
| Keyword:
|
left idempotency |
| MSC:
|
08A30 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1106.20049 |
| idMR:
|
MR2175855 |
| . |
| Date available:
|
2009-05-05T16:49:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119504 |
| . |
| Reference:
|
[1] Dehornoy P.: Braids and Self Distributivity.Progress in Mathematics, vol. 192, Birkhäuser, 2000. Zbl 0958.20033, MR 1778150 |
| Reference:
|
[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. |
| Reference:
|
[3] Kepka T.: Non-idempotent left symmetric left distributive groupoids.Comment. Math. Univ. Carolinae 35 1 181-186 (1994). Zbl 0807.20057, MR 1292593 |
| Reference:
|
[4] Kepka T.: Notes on left distributive groupoids.Acta Univ. Carolinae Math. Phys. 22.2 (1981), 23-37. Zbl 0517.20048, MR 0654379 |
| Reference:
|
[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 |
| Reference:
|
[6] Stanovský D.: Homomorphic images of subdirectly irreducible algebras.Contest Thesis, 2001, http://www.karlin.mff.cuni.cz/\char126stanovsk/math/publ.htm. |
| . |
