| Title:
|
Commutators and associators in Catalan loops (English) |
| Author:
|
Raasch, Jan M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
333-347 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops. (English) |
| Keyword:
|
loop |
| Keyword:
|
right loop |
| Keyword:
|
left loop |
| Keyword:
|
commutator |
| Keyword:
|
associator |
| MSC:
|
20F12 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20066 |
| idMR:
|
MR2682485 |
| . |
| Date available:
|
2010-05-21T12:51:46Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140111 |
| . |
| Reference:
|
[1] Balcerzyk S., Józefiak T.: Commutative Noetherian and Krull Rings.PWN, Warsaw, 1989. MR 1130610 |
| Reference:
|
[2] Bruck R.H.: A Survey of Binary Systems.Springer, Berlin, 1958. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[3] Coxeter H.S.M., Moser W.O.J.: Generators and Relations for Discrete Groups.Springer, Berlin, 1957. Zbl 0487.20023, MR 0088489 |
| Reference:
|
[4] Long L., Smith J.D.H.: Catalan loops.preprint, 2009. |
| Reference:
|
[5] Mac Lane S.: Homology.Springer, Berlin, 1963. Zbl 0818.18001 |
| . |
