Evolution algebras and their three-dimensional chains (PhD dissertation discussion)

This dissertation is devoted to study finite-dimensional evolution algebras, evolution algebras corresponding to permutations and classification of real evolution algebras in three-dimensional chains. In this dissertation, we give a necessary and sufficient condition for $n$-dimensional evolution algebras, which rank of matrix of structural constants equals to $n-2$, to have a unique absolute nilpotent element. We present creterions for evolution algebras corresponding to permutations to be baric and nil. We fully describe their absolute nilpotent and idempotent elements. We give classification of algebras in some chains of evolution algebras.