About the embedding of Moufang loops in alternative algebras II
| dc.creator | Sandu, N. I. | |
| dc.date | 2008-04-13 | |
| dc.date.accessioned | 2026-07-07T09:32:09Z | |
| dc.date.available | 2026-07-07T09:32:09Z | |
| dc.description | It is known that with precision till isomorphism that only and only loops $M(F) = M_0(F)/<-1>$, where $M_0(F)$ denotes the loop, consisting from elements of all matrix Cayley-Dickson algebra $C(F)$ with norm 1, and $F$ be a subfield of arbitrary fixed algebraically closed field, are simple non-associative Moufang loops. In this paper it is proved that the simple loops $M(F)$ they and only they are not embedded into a loops of invertible elements of any unitaly alternative algebras if $\text{char} F \neq 2$ and $F$ is closed under square root operation. For the remaining Moufang loops such an embedding is possible. Using this embedding it is quite simple to prove the well-known finding: the finite Moufang $p$-loop is centrally nilpotent. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0804.2049 | |
| dc.identifier | http://arxiv.org/abs/0804.2049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158712 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17D05; 20N05 | |
| dc.title | About the embedding of Moufang loops in alternative algebras II | |
| dc.type | text |