Topological rank of (-1, 1) metabelian algebras
Resumen
In 1981, Pchelintsev developed the idea for arranging non-nilpotent subvarieties in a given variety by using topological rank for spechtian varieties of algebra as a fixed tool. In this paper we show that for a given topological rank over a field of 2, 3 ? torsion free of (-1; 1) metabelian algebra solvable of index 2 that are Lie-nilpotent of step not more than p is equal to P.
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Badeev, A. V., the variety N3N2 of commutative alternative nil-algebras of index 3 over a field of charcterstic3, Fundam. Prikl. Mat. 8 335-336 Russian(2002).
Kuz'min, A. M., On Spechtian Varieties of right alternative algebras, J. Math. Sci., New York 149 1098-1106 1098-1106; translation from Fundam. Prikl. Mat. 12 89-100, (2006). https://doi.org/10.1007/s10958-008-0048-6
Il'tyakov, A. V., On finite basis of identities of Lie algebra representations, Nova J. Algebra Geom. 1 207-259, (1992).
Il'tyakov, A. V., Finiteness of basis of identities of a finitely generated alternative PI-algebra over a field of characteristic zero, Sib. Math. J. 32, 948-961 (1991) https://doi.org/10.1007/BF00971199 translation from Sib. Mat. Zh. 32 61-76,(1991).
Belov, A.Ya., Conterexamples to the Specht problem, Sb. Math. 191 329-340, (2000) https://doi.org/10.1070/SM2000v191n03ABEH000460 translation form Mat.sb.191 13-14, (2000). https://doi.org/10.4213/sm490
Vais A.Ya., Zel'manov, E. I., Kemer's theorem for finitly generated Jordan algebras, Sov. Math. 33 38-47, (1989) translation from Izv. Vyssh. Uchebn. Zaved. Mat. 6 42-51, (1989).
Isaev, I. M., Finite-dimensional right alternative algebras that do not generate finitly based varietities , Algebra Logic 25 86-96, (1986) translation from Algebra Logika 25 136-153, (1986). https://doi.org/10.1007/BF01978883
Jayalakshmi, K., and Hari babu, K., (-1, 1) metabelian rings , Bol. Soc. Paran. Mat. (3s.) v. 35 2 115-125, (2017). https://doi.org/10.5269/bspm.v35i2.26250
Zhavlakov, K. N., Slin'ko, A. M., Shestakov, I.P., and Shirshov, A.I., Rings that are nearly associative, translated from the Russian by Harry F.Smith.(Acedamic press,Inc., New York- London, (1982).
Pchelintsev, S. V., On identities of right alternative metabelian grassmann algebras, J. Math. Sci., New York 154 230-248,(2008) https://doi.org/10.1007/s10958-008-9162-8 translation from Fundam. Prikl. Mat. 13 157-183, (2007).
Pchelintsev, S. V., Varieties of algebras that are solvable of index 2, Math. USSR, Sb 43 159-180, (1982) https://doi.org/10.1070/SM1982v043n02ABEH002442 translation from Mat. Sb. 115 (157) 179-203 (1981).
Platonova, S. V., Varieties of two- step solvable algebras of type (γ, δ), J. Math. Sci., New York 139 6762-6779, (2006) https://doi.org/10.1007/s10958-006-0389-y translation from Fundam. Prikl. Mat. 10 157-180, (2004).
Belkin, V. P., Varietities of right alternative algebras, Algebra Logic 15 309-320, (1976) https://doi.org/10.1007/BF02069105 translation from Algebra Logika 15 491-508, (1976).
Medvedev, Yu. A., Example of a variety of solvable alternative algebras over a field of characteristic 2 having no finite basis of identities, Algebra Logic 19 191-201, (1980) https://doi.org/10.1007/BF01668996 translation from Algebra Logika 19 300-313, (1980).
Medvedev, Yu. A., Finite basis theorem on varieties with a 2- term identity, Algebra Logic 17 458-472, (1978) https://doi.org/10.1007/BF01673576 translation from Algebra Logika 17 705-726, (1978).
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Funding data
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University Grants Commission
Grant numbers 42-17 (2013)
