Right alternative superalgebras of capacity 1 with strongly alternative even part
Algebra i logika, Tome 59 (2020) no. 2, pp. 260-281.

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We look at the structure of a unital right alternative superalgebra of capacity 1 over an algebraically closed field assuming that its even part is finite-dimensional and strongly alternative. It is proved that the condition of being simple for such a superalgebra implies the simplicity of its even part.
Keywords: right alternative superalgebra, superalgebra of capacity 1, simple superalgebra.
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O. V. Shashkov. Right alternative superalgebras of capacity 1 with strongly alternative even part. Algebra i logika, Tome 59 (2020) no. 2, pp. 260-281. http://geodesic.mathdoc.fr/item/AL_2020_59_2_a5/

[1] E. I. Zelmanov, I. P. Shestakov, “Pervichnye alternativnye superalgebry i nilpotentnost radikala svobodnoi alternativnoi algebry”, Izv. AN SSSR. Ser. matem., 54:4 (1990), 676–693 | Zbl

[2] C. T. C. Wall, “Graded Brauer groups”, J. Reine Angew. Math., 213 (1964), 187–199 | MR | Zbl

[3] I. P. Shestakov, “Pervichnye alternativnye superalgebry proizvolnoi kharakteristiki”, Algebra i logika, 36:6 (1997), 675–716 | MR | Zbl

[4] I. P. Shestakov, “Prostye $(-1,1)$-superalgebry”, Algebra i logika, 37:6 (1998), 721–739 | MR | Zbl

[5] A. A. Albert, “On right alternative algebras”, Ann. Math. (2), 50 (1949), 318–328 | MR | Zbl

[6] J. P. da Silva, L. S. I. Murakami, I. Shestakov, “On right alternative superalgebras”, Commun. Algebra, 44:1 (2016), 240–252 | MR | Zbl

[7] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye superalgebry s unitarnoi chetnoi chastyu nad polem kharakteristiki 0”, Matem. zametki, 100:4 (2016), 577–585 | Zbl

[8] L. S. I. Murakami, S. V. Pchelintsev, O. V. Shashkov, “Finite-dimensional right alternative superalgebras with semisimple strongly alternative even part”, J. Algebra, 528 (2019), 150–176 | MR | Zbl

[9] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye superalgebry abeleva tipa kharakteristiki nul”, Izv. RAN. Cer. matem., 79:3 (2015), 131–158 | MR | Zbl

[10] S. V. Pchelintsev, O. V. Shashkov, “Prostye pravoalternativnye superalgebry abeleva tipa, chetnaya chast kotorykh yavlyaetsya polem”, Izv. RAN. Cer. matem., 80:6 (2016), 247–257 | MR | Zbl

[11] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye superalgebry s poluprostoi silno assotsiativnoi chetnoi chastyu”, Matem. sb., 208:2 (2017), 55–69 | Zbl

[12] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye unitalnye superalgebry s silno assotsiativnoi chetnoi chastyu”, Matem. sb., 208:4 (2017), 73–86 | Zbl

[13] S. V. Pchelintsev, O. V. Shashkov, “Prostye konechnomernye pravoalternativnye unitalnye superalgebry s assotsiativno-kommutativnoi chetnoi chastyu nad polem kharakteristiki nul”, Izv. RAN. Ser. matem., 82:3 (2018), 136–153 | MR | Zbl

[14] R. D. Schafer, “Alternative algebras over an arbitrary field”, Bull. Am. Math. Soc., 49 (1943), 549–555 | MR | Zbl

[15] M. Zorn, “Alternative rings and related questions. I. Existence of the radical”, Ann. Math., Princeton, (2), 42 (1941), 676–686 | MR

[16] M. Zorn, “Theorie der alternativen ringe”, Abhandlungen Hamburg, 8 (1930), 123–147 | MR | Zbl

[17] N. Jacobson, “Structure of alternative and Jordan bimodules”, Osaka Math. J., 6 (1954), 1–71 | MR | Zbl