Geodesic
Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras
Algebra i logika, Tome 61 (2022) no. 6, pp. 742-765.

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It is proved that a singular superalgebra with a $2$-dimensional even part is isomorphic to a superalgebra $B_{2\mid3}(\varphi,\xi,\psi)$. In particular, there do not exist infinite-dimensional simple singular superalgebra with a $2$-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number $N\geq 5$, except the numbers $6,7,8,11$, there exist singular superalgebras with a switch of dimension $N$. For the numbers $N=6,7,8,11$, there do not exist singular $N$-dimensional superalgebras with a switch.
Keywords: singular superalgebra with switch, extended double, singular superalgebra with $2$-dimensional even part. 
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S. V. Pchelintsev; O. V. Shashkov. Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras. Algebra i logika, Tome 61 (2022) no. 6, pp. 742-765. http://geodesic.mathdoc.fr/item/AL_2022_61_6_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] J. P. da Silva, L. S. I. Murakami, I. Shestakov, “On right alternative superalgebras”, Commun. Algebra, 44:1 (2016), 240–252 | DOI | MR | Zbl

[3] S. V. Pchelintsev, O. V. Shashkov, “Prostye 5-mernye pravoalternativnye superalgebry s trivialnoi chetnoi chastyu”, Sib. matem. zh., 58:6 (2017), 1387–1400 | MR | Zbl

[4] S. V. Pchelintsev, O. V. Shashkov, “Singulyarnye 6-mernye superalgebry”, Sib. elektron. matem. izv., 15 (2018), 92–105 http://semr.math.nsc.ru/v15/p92-105.pdf | Zbl

[5] S. V. Pchelintsev, O. V. Shashkov, “Linearly generated singular superalgebras”, J. Algebra, 546 (2020), 580–603 | DOI | MR | Zbl

[6] S. V. Pchelintsev, O. V. Shashkov, “Algebraicheski porozhdennye superalgebry”, Izv. vuzov. Matem., 2021, no. 6, 67–83 | Zbl

[7] E. Kleinfeld, “Right alternative rings”, Proc. Am. Math. Soc., 4 (1953), 939–944 | DOI | MR | Zbl

[8] A. I. Maltsev, Osnovy lineinoi algebry, Lan, Sankt-Peterburg, 2009 | MR

[9] N. Dzhekobson, Algebry Li, Mir, M., 1964 \pagebreak

[10] S. Leng, Algebra, Mir, M., 1968