Abstract:
An algebra obtained by the external adjoining a unit to a nilalgebra is said to be unitary. It is proved that every simple finite-dimensional right alternative superalgebra with unitary even part over a field of characteristic 00 is associative.
Keywords:
simple superalgebra, simple finite-dimensional right alternative superalgebra, unital superalgebra, radical.
Citation:
S. V. Pchelintsev, O. V. Shashkov, “Simple Finite-Dimensional Right Alternative Superalgebras with Unitary Even Part over a Field of Characteristic 00”, Mat. Zametki, 100:4 (2016), 577–585; Math. Notes, 100:4 (2016), 589–596
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\paper Simple Finite-Dimensional Right Alternative Superalgebras with Unitary Even Part over a Field of Characteristic~$0$
\jour Mat. Zametki
\yr 2016
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\issue 4
\pages 577--585
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\jour Math. Notes
\yr 2016
\vol 100
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\pages 589--596
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Linking options:
https://www.mathnet.ru/eng/mzm10880
https://doi.org/10.4213/mzm10880
https://www.mathnet.ru/eng/mzm/v100/i4/p577
This publication is cited in the following 12 articles:
S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras”, J. Math. Sci., 284:4 (2024), 527–544
O. V. Shashkov, “Right alternative superalgebras of capacity 1 with strongly alternative even part”, Algebra and Logic, 59:2 (2020), 180–195
S. V. Pchelintsev, O. V. Shashkov, “Simple right-alternative superalgebras with semisimple even part”, Siberian Math. J., 61:2 (2020), 304–321
O. V. Shashkov, “Finite-dimensional unital right alternative superalgebras with strongly alternative even part”, Siberian Math. J., 61:5 (2020), 926–940
O. V. Shashkov, “Ob osnovnoi teoreme Vedderberna dlya pravoalternativnykh superalgebr emkosti $1$”, Sib. elektron. matem. izv., 17 (2020), 1571–1579
S. V. Pchelintsev, O. V. Shashkov, “Linearly generated singular superalgebras”, J. Algebra, 546 (2020), 580–603
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
S. V. Pchelintsev, O. V. Shashkov, “Simple right-alternative unital superalgebras over an algebra of matrices of order $2$”, Algebra and Logic, 58:1 (2019), 77–94
S. V. Pchelintsev, O. V. Shashkov, “Singulyarnye 6-mernye superalgebry”, Sib. elektron. matem. izv., 15 (2018), 92–105
S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras
with associative-commutative even part over a field of characteristic zero”, Izv. Math., 82:3 (2018), 578–595
S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras with strongly associative even part”, Sb. Math., 208:4 (2017), 531–545
S. V. Pchelintsev, O. V. Shashkov, “Simple $5$-dimensional right alternative superalgebras with trivial even part”, Siberian Math. J., 58:6 (2017), 1078–1089
Citation in format AMSBIB
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