Geodesic
Structure of finitely generated commutative alternative algebras and special Moufang loops
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 413-420

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the commutator ideal of the multiplication algebra of a free commutative alternative algebra of rank $n$ is nilpotent of index $n-1$. As a corollary to this fact, the Bruck theorem for special commutative Moufang loops is derived.
Keywords: commutative Moufang loop, central nilpotency, alternative algebra, special Moufang loop. 
@article{MZM_2006_80_3_a10,
     author = {S. V. Pchelintsev},
     title = {Structure of finitely generated commutative alternative algebras and special {Moufang} loops},
     journal = {Matemati\v{c}eskie zametki},
     pages = {413--420},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a10/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
TI  - Structure of finitely generated commutative alternative algebras and special Moufang loops
JO  - Matematičeskie zametki
PY  - 2006
SP  - 413
EP  - 420
VL  - 80
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a10/
LA  - ru
ID  - MZM_2006_80_3_a10
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%T Structure of finitely generated commutative alternative algebras and special Moufang loops
%J Matematičeskie zametki
%D 2006
%P 413-420
%V 80
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a10/
%G ru
%F MZM_2006_80_3_a10
S. V. Pchelintsev. Structure of finitely generated commutative alternative algebras and special Moufang loops. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 413-420. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a10/