Geodesic
Simple right-symmetric $(1,1)$-superalgebras
Algebra i logika, Tome 60 (2021) no. 2, pp. 166-175

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

It is proved that $2$-torsion-free prime right-symmetric superrings having a nontrivial idempotent and satisfying a superidentity $(x,y,z)+(-1)^{z(x+y)}\cdot (z,x,y)+(-1)^{x(y+z)}(y,z,x)=0$ are associative. As a consequence, every simple finite-dimensional $(1,1)$-superalgebra with semisimple even part over an algebraically closed field of characteristic $0$ is associative.
Keywords: right-symmetric ring, left-symmetric algebra, pre-Lie algebra, prime ring, Peirce decomposition, $(1,1)$-superalgebra. 
@article{AL_2021_60_2_a3,
     author = {A. P. Pozhidaev and I. P. Shestakov},
     title = {Simple right-symmetric $(1,1)$-superalgebras},
     journal = {Algebra i logika},
     pages = {166--175},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_2_a3/}
}
TY  - JOUR
AU  - A. P. Pozhidaev
AU  - I. P. Shestakov
TI  - Simple right-symmetric $(1,1)$-superalgebras
JO  - Algebra i logika
PY  - 2021
SP  - 166
EP  - 175
VL  - 60
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2021_60_2_a3/
LA  - ru
ID  - AL_2021_60_2_a3
ER  - 
%0 Journal Article
%A A. P. Pozhidaev
%A I. P. Shestakov
%T Simple right-symmetric $(1,1)$-superalgebras
%J Algebra i logika
%D 2021
%P 166-175
%V 60
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2021_60_2_a3/
%G ru
%F AL_2021_60_2_a3
A. P. Pozhidaev; I. P. Shestakov. Simple right-symmetric $(1,1)$-superalgebras. Algebra i logika, Tome 60 (2021) no. 2, pp. 166-175. http://geodesic.mathdoc.fr/item/AL_2021_60_2_a3/