Topological rank of (-1, 1) metabelian algebras

  • Karamsi Jayalakshmi Jawaharlal Nehru technological University Ananthapur
  • Kommaddi Hari Babu Jawaharlal Nehru Technological University

Abstract

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.

Downloads

Download data is not yet available.

Author Biographies

Karamsi Jayalakshmi, Jawaharlal Nehru technological University Ananthapur
Mathematics
Kommaddi Hari Babu, Jawaharlal Nehru Technological University

Mathematics

References

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).

Published
2021-12-17
Section
Articles

Funding data