| Title:
|
On Equational Theory of Left Divisible Left Distributive Groupoids (English) |
| Author:
|
Jedlička, Přemysl |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
67-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping $a\mapsto a^2$ surjective lies in the variety generated by the left distributive left quasigroups. (English) |
| Keyword:
|
left distributivity |
| Keyword:
|
left idempotency |
| Keyword:
|
variety |
| MSC:
|
20N02 |
| MSC:
|
20N05 08B15 |
| idZBL:
|
Zbl 06204931 |
| idMR:
|
MR3058874 |
| . |
| Date available:
|
2012-11-26T10:18:32Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143068 |
| . |
| Reference:
|
[1] Barboriková, J.: Systémy automatického dokazování (Systems of automated reasoning). bachelor thesis, Charles University, Praha, 2009, (in Czech). |
| Reference:
|
[2] Dehornoy, P.: Braids and Self-Distributivity. Progress in Mathematics 192, Birkhäuser, Basel, 2000. Zbl 0958.20033, MR 1778150 |
| Reference:
|
[3] Drápal, A., Kepka, T., Musílek, M.: Group Conjugation has Non-Trivial LD-Identities. Comment. Math. Univ. Carol. 35 (1994), 219–222. Zbl 0810.20053, MR 1286567 |
| Reference:
|
[4] Jedlička, P.: On left distributive left idempotent groupoids. Comm. Math. Univ. Carol. 46, 1 (2005), 15–20. Zbl 1106.20049, MR 2175855 |
| Reference:
|
[5] Joyce, D.: A Classifying Invariant of Knots, the Knot Quandle. J. Pure App. Alg. 23 (1982), 37–56. Zbl 0474.57003, MR 0638121, 10.1016/0022-4049(82)90077-9 |
| Reference:
|
[6] Kepka, T.: Notes On Left Distributive Groupoids. Acta Univ. Carolinae – Math. et Phys. 22, 2 (1981), 23–37. Zbl 0517.20048, MR 0654379 |
| Reference:
|
[7] Larue, D.: Left-Distributive Idempotent Algebras. Commun. Alg. 27, 5 (1999), 2003–2029. Zbl 0940.20070, MR 1683848, 10.1080/00927879908826547 |
| Reference:
|
[8] Stanovský, D.: On the equational theory of group conjugation. In: Contributions to General Algebra 15, Heyn, Klagenfurt, 2004, 177–185. Zbl 1076.20062, MR 2082381 |
| . |
