TY - JOUR

T1 - Сentral orders in simple finite dimensional superalgebras

AU - PANASENKO, Alexander Sergeevich

N1 - Funding Information: The work is supported by Mathematical Center in Akademgorodok, the agreement with Ministry of Science and High Education of the Russian Federation number 075-15-2019-1613. The reported study was funded by RFBR, project number 19-31-90055. The author is grateful to the referee for the useful comments. The author also expresses his gratitude to P. S. Kolesnikov, whose remarks helped to improve this paper.

PY - 2020

Y1 - 2020

N2 - The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely generated module over its center. An analogue of this theorem for alternative and Jordan algebras was earlier proved by V.N. Zhelyabin and the author. In this paper we discuss this problem for associative, classical Jordan and some alternative superalgebras.

AB - The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely generated module over its center. An analogue of this theorem for alternative and Jordan algebras was earlier proved by V.N. Zhelyabin and the author. In this paper we discuss this problem for associative, classical Jordan and some alternative superalgebras.

KW - alternatve superalgebra

KW - associative superalgebra

KW - central order

KW - Jordan superalgebra

KW - simple superalgebra

UR - http://www.scopus.com/inward/record.url?scp=85099259713&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.077

DO - 10.33048/semi.2020.17.077

M3 - Article

AN - SCOPUS:85099259713

VL - 17

SP - 1027

EP - 1042

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -