Genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. This paper investigates the existence of non-associative and derivation of genetic algebra related to some operators generated by ξ (as) − QSO. Moreover, a transformation of genetic algebra to some evolution algebras in dimension four is investigated.

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In the theory of non-associative algebras, particularly in genetic algebras, Lie algebra. The derivations of a given algebra are one of the important tools for studying its structure. This work investigates the derivations of n-dimensional complex evolution algebras based on the rank of appropriate matrices. The spaces of derivations of evolution algebras under some possible conditions with matrices of rank n-2 are investigated.

This work investigates the derivations of n-dimensional complex evolution algebras, based on the rank of the structural matrix. The spaces of the derivations of evolution algebras under three different conditions that make the rank of the structural matrix equals to n − 2 are investigated.