  We consider the structure of groups and algebras that can be represented as
automorphisms or derivations of distributive products -- which includes
nonassociative rings, modules, forms, and commutation of groups and
nonassociative loops. In many ways this is too broad to be possible, for
instance even naive structure, such as inner automorphisms and derivations, are
undefined for general bilinear maps. The appeal for working in this generality
is broad applicability. We introduce fundamental structures and prove several
results akin to ones in ring theory, including theorems of Morita and of
Skolem-Noether type. Applications and examples are included.
