  We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an
evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a
previous work, maximal ideals have been related to hereditary subsets of a
graph associated to the given algebra. We investigate the superfluous members
both in the family of maximal ideals and also in the set of hereditary subsets
of the associated graphs. By using subdirect products we state a structure
theorem for arbitrary evolution algebras (arbitrary dimensions and ground
field). Specializing in the perfect finite-dimensional case, we obtain a direct
sum decomposition instead of a subdirect product and also a uniqueness
property. We also study some examples in which Grassmanians appear in a natural
way and others that exhibit a richer structure with a nonzero semisimple part
that is non-associative.
