Some properties of evolution algebras
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1481-1494
Printed September 1, 2013
L. M. Camacho, J. R. G\'omez, B. A. Omirov, and R. M. Turdibaev
Universidad de Sevilla, Universidad de Sevilla, Institute of Mathematics and Information Technologies, National University of Uzbekistan
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, nilpo\-tency
MSC numbers : 05C25, 17A36, 17D92, 17D99
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