  In the present paper we study some algebraic properties of evolution
algebras. Moreover, we reduce the study of evolution algebras of permutations
to two special types of evolution algebras, idempotents and absolute nilpotent
elements of the algebra. We study three-dimensional evolution algebras whose
each element of evolution basis has infinite period. In addition, for an
evolution algebra with some properties we describe its associative enveloping
algebra.
