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

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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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     author = {V. N. Zhelyabin and A. S. Panasenko},
     title = {Herstein's construction for just infinite superalgebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1317--1323},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a39/}
}
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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/