Geodesic
Herstein's construction for just infinite superalgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1317-1323.

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

The connections between semiprime associative $Z_{2}$-graded algebras and Jordan superalgebras are studied. It is proved that if an adjoint Jordan superalgebra $B^{(+)_{s}}$ to an associative noncommutative $Z_{2}$-graded semiprime superalgebra $B$ contains an ideal, consisted of odd elements, then the center of algebra $B$ contains a nonzero ideal. Besides, this ideal annihilates every commutator of the algebra $B$. As a corollary we have that if a $Z_{2}$-graded algebra $B$ is just infinite then a Jordan superalgebra $B^{(+)_{s}}$ is just infinite.
Mots-clés : associative algebras
Keywords: Jordan superalgebras, just infinite algebras, semiprime algebras. 
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V. N. Zhelyabin; A. S. Panasenko. Herstein's construction for just infinite superalgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1317-1323. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a39/

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