S. V. Pchelintsev, O. V. Shashkov, “Algebraically generated superalgebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 6, 67–83; Russian Math. (Iz. VUZ), 65:6 (2021), 57

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 6, Pages 67–83
DOI: https://doi.org/10.26907/0021-3446-2021-6-67-83 (Mi ivm9687)

This article is cited in 5 scientific papers (total in 5 papers)

Algebraically generated superalgebras

S. V. Pchelintsev^ab, O. V. Shashkov^a

^a Financial University under the Government of the Russian Federation, 49 Leningradsky Ave., Moscow, 125167 Russia
^b Moscow State University, 1 Lenin Hills, Moscow, 119991 Russia

Full-text PDF (404 kB) Citations (5)

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DOI: https://doi.org/10.26907/0021-3446-2021-6-67-83

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 a 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 a non-degenerate switch is an extended double. It is also shown that for any number

d \geq 32

$d\geq32$ there exists a

d

$d$ -dimensional extended double.

Keywords: simple right-alternative superalgebra, singular superalgebra, non-degenerate switch, extended double.

Funding agency	Grant number
Moscow Center of Fundamental and Applied Mathematics

Received: 21.06.2020
Revised: 12.09.2020
Accepted: 01.10.2020

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 6, Pages 57–72
DOI: https://doi.org/10.3103/S1066369X21060074

Document Type: Article

UDC: 512.554

Language: Russian

Citation: S. V. Pchelintsev, O. V. Shashkov, “Algebraically generated superalgebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 6, 67–83; Russian Math. (Iz. VUZ), 65:6 (2021), 57–72

Citation in format AMSBIB

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\by S.~V.~Pchelintsev, O.~V.~Shashkov

\paper Algebraically generated superalgebras

\jour Izv. Vyssh. Uchebn. Zaved. Mat.

\yr 2021

\issue 6

\pages 67--83

\mathnet{http://mi.mathnet.ru/ivm9687}

\crossref{https://doi.org/10.26907/0021-3446-2021-6-67-83}

\transl

\jour Russian Math. (Iz. VUZ)

\yr 2021

\vol 65

\issue 6

\pages 57--72

\crossref{https://doi.org/10.3103/S1066369X21060074}

Linking options:

https://www.mathnet.ru/eng/ivm9687

https://www.mathnet.ru/eng/ivm/y2021/i6/p67

This publication is cited in the following 5 articles:

Sergey Pchelintsev, Oleg Shashkov, “A finite-dimensional singular superalgebra is algebraically generated”, Journal of Algebra, 645 (2024), 86
O. M. Drapkina, R. N. Shepel, A. V. Korotkova, Yu. S. Naumova, G. O. Hagverdiyev, A. A. Shcherbinsky, M. M. Sachek, G. U. Kulkaeva, N. N. Brimkulov, G. M. Muhsinzoda, I. R. Uralieva, E. Yu. Ogneva, “Development of various aspects of primary health care in the context of national health systems of the Commonwealth of Independent States. Part 2: management of primary health care subsystems, structural elements, processes”, PMSP, 1:2 (2024), 6
S. V. Pchelintsev, O. V. Shashkov, “Structure of Singular Superalgebras with 2-Dimensional Even Part and New Examples of Singular Superalgebras”, Algebra Logic, 61:6 (2023), 506
S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras”, J. Math. Sci., 284:4 (2024), 527–544
S. V. Pchelintsev, O. V. Shashkov, “Stroenie singulyarnykh superalgebr s $2$ -mernoi chetnoi chastyu i novye primery singulyarnykh superalgebr”, Algebra i logika, 61:6 (2022), 742–765

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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