| Title:
|
F-quasigroups and generalized modules (English) |
| Author:
|
Kepka, Tomáš |
| Author:
|
Kinyon, Michael K. |
| Author:
|
Phillips, J. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
249-257 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In Kepka T., Kinyon M.K., Phillips J.D., {\it The structure of F-quasigroups\/}, J. Algebra {\bf 317} (2007), 435--461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring. (English) |
| Keyword:
|
F-quasigroup |
| Keyword:
|
Moufang loop |
| Keyword:
|
generalized modules |
| MSC:
|
16Y99 |
| MSC:
|
17A30 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1192.20055 |
| idMR:
|
MR2426889 |
| . |
| Date available:
|
2009-05-05T17:11:03Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119719 |
| . |
| Reference:
|
[1] Bruck R.H.: A Survey of Binary Systems.Springer, 1971. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[2] Bruck R.H., Paige L.: Loops in which every inner mapping is an automorphism.Ann. of Math. 63 (1956), 308-323. MR 0076779, 10.2307/1969612 |
| Reference:
|
[3] Kepka T., Kinyon M.K., Phillips J.D.: The structure of F-quasigroups.J. Algebra 317 (2007), 435-461. Zbl 1133.20051, MR 2362925, 10.1016/j.jalgebra.2007.05.007 |
| Reference:
|
[4] Moufang R.: Zur Struktur von Alternativkörpern.Math. Ann. 110 (1935), 416-430. MR 1512948, 10.1007/BF01448037 |
| Reference:
|
[5] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Helderman, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| . |
