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Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 1317–1323 (Mi semr872)  

Mathematical logic, algebra and number theory

Herstein's construction for just infinite superalgebras

V. N. Zhelyabinab, A. S. Panasenkoba

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova st., 1, 630090, Novosibirsk, Russia

Abstract: 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.

Keywords: associative algebras, Jordan superalgebras, just infinite algebras, semiprime algebras.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065


DOI: https://doi.org/10.17377/semi.2017.14.112

Full text: PDF file (133 kB)
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Bibliographic databases:

UDC: 512.554.7
MSC: 17C70
Received October 21, 2017, published December 6, 2017

Citation: V. N. Zhelyabin, A. S. Panasenko, “Herstein's construction for just infinite superalgebras”, Sib. Èlektron. Mat. Izv., 14 (2017), 1317–1323

Citation in format AMSBIB
\Bibitem{ZhePan17}
\by V.~N.~Zhelyabin, A.~S.~Panasenko
\paper Herstein's construction for just infinite superalgebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 1317--1323
\mathnet{http://mi.mathnet.ru/semr872}
\crossref{https://doi.org/10.17377/semi.2017.14.112}


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