Biderivations of some evolution algebras

The purpose of this paper is to prove that any biderivations of n-dimensional complex evolution algebras depend on the rank of the appropriate matrices. For evolution algebras with non-singular matrices, we prove that any biderivation is the zero mapping. All biderivations for evolution algebras with matrices of rank n − 1 are described. Additionally, we characterize all biderivations of nilpotent n-dimensional evolution algebras over an arbitrary field of characteristic zero.