| Title:
|
When is it hard to show that a quasigroup is a loop? (English) |
| Author:
|
Keedwell, A. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
241-247 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We contrast the simple proof that a quasigroup which satisfies the Moufang identity $(x\cdot yz)x = xy\cdot zx$ is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity $(xy\cdot z)y=x(y\cdot zy)$ is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity. (English) |
| Keyword:
|
Moufang quasigroups |
| Keyword:
|
Moufang loops |
| Keyword:
|
identities of Bol-Moufang type |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1192.20054 |
| idMR:
|
MR2426888 |
| . |
| Date available:
|
2009-05-05T17:10:58Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119718 |
| . |
| Reference:
|
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|
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| Reference:
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| . |
