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This article is cited in 8 scientific papers (total in 9 papers)
Solvable just-non-Cross varieties of Lie rings
Yu. A. Bahturin, A. Yu. Ol'shanskii
Abstract:
A variety of Lie rings is called just-non-Cross if it itself is not Cross, but each of its proper subvarieties is Cross, i.e. is generated by a finite ring. In this paper, we completely describe the solvable just-non-Cross varieties both of Lie rings and of Lie $R$-algebras where $R$ is a finite commutative ring with identity and, in particular, where $R$ is a finite field. We find algorithms which allow us to determine whether a given identity defines a Cross variety of Lie algebras; also, using the multiplication and addition tables of a finite Lie algebra, we find algorithms for extracting its identities.
Bibliography: 10 titles.
Received: 18.04.1975
Citation:
Yu. A. Bahturin, A. Yu. Ol'shanskii, “Solvable just-non-Cross varieties of Lie rings”, Mat. Sb. (N.S.), 100(142):3(7) (1976), 384–399; Math. USSR-Sb., 29:3 (1976), 345–358
Linking options:
https://www.mathnet.ru/eng/sm2879https://doi.org/10.1070/SM1976v029n03ABEH003672 https://www.mathnet.ru/eng/sm/v142/i3/p384
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Abstract page: | 420 | Russian version PDF: | 99 | English version PDF: | 18 | References: | 66 | First page: | 2 |
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