Abstract
A simple right-alternative superalgebra whose even part has zero multiplication is called singular. In the paper, finite-dimensional algebraically generated singular superalgebras with non-degenerate switch are introduced and studied. A special case of such algebras, namely, linearly generated superalgebras, was previously classified by the authors. The construction of the extended double is given in the paper and it is proved that an algebraically generated singular superalgebra with non-degenerate switch is an extended double. It is also shown that, for any number \(d\geq32\), there exists a d-dimensional extended double.
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ACKNOWLEDGMENTS
The authors wish to express their gratitude to the referee for careful reading of this paper and useful remarks. The first author wishes to express his gratitude to the Moscow University Center of Fundamental and Applied Mathematics for financial support.
Funding
The first author was supported by the Moscow University Center of Fundamental and Applied Mathematics, the Grant “Structure theory and combinatorial-logical methods in the theory of algebraic systems”.
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 6, pp. 67–83.
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Pchelintsev, S.V., Shashkov, O.V. Algebraically Generated Superalgebras. Russ Math. 65, 57–72 (2021). https://doi.org/10.3103/S1066369X21060074
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DOI: https://doi.org/10.3103/S1066369X21060074