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http://dx.doi.org/10.4134/BKMS.2013.50.5.1481

SOME PROPERTIES OF EVOLUTION ALGEBRAS  

Camacho, L.M. (Dpto. Matematica Aplicada I Universidad de Sevilla)
Gomez, J.R. (Universidad de Sevilla)
Omirov, B.A. (Institute of Mathematics and Information Technologies)
Turdibaev, R.M. (Department of Mathematics National University of Uzbekistan)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1481-1494 More about this Journal
Abstract
The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}$.
Keywords
evolution algebra; commutative algebra; isomorphism; nilpotency;
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