  The paper defines the notion of alternative loop algebra F[Q] for any
nonassociative Moufang loop Q as being any non-zero homomorphic image of the
loop algebra FQ of a loop Q over a field F. For the class M of all
nonassociative alternative loop algebras F[Q] and for the class L of all
nonassociative Moufang loops Q are defined the radicals R and S, respectively.
Moreover, for classes M, L is proved an analogue of Wedderburn Theorem for
finite dimensional associative algebras. It is also proved that any Moufang
loop Q from the radical class R can be embedded into the loop of invertible
elements U(F[Q])of alternative loop algebra F[Q]. The remaining loops in the
class of all nonassociative Moufang loops L cannot be embedded into loops of
invertible elements of any unital alternative algebras.
