Lower bounds for the length of non associative algebras

Sudha Lakshmi.G; Akshaya.G

doi:https://doi.org/10.14445/22315373/IJMTT-V66I1P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P521

Lower bounds for the length of non associative algebras

Sudha Lakshmi.G, Akshaya.G

Citation :

Sudha Lakshmi.G, Akshaya.G, "Lower bounds for the length of non associative algebras," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 169-174, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P521

Abstract

We obtain a sharp lower bound for the length of arbitrary non- associative algebra and present an example demonstrating the sharpness of our bound. To show this we introduce a new method of characteristic sequences based on linear algebra technique. This method provides an efficient tool for computing the length function in non-associative case. Then we apply anothermethod to obtain an lower bound for the length of an arbitrary locally complex algebra. We also show that the obtained bound is sharp. In the last case the length is bounded in terms of Fibonacci sequence.

Keywords

Finite subset, locally complex, linear span, finite dimensional

References

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