ABSTRACT
A polynomial identity _F(Xi,. . . , X n) can be considered as an element of the free (associative) algebra with n generators, i.e. the tensor algebra T(V), where V = { X i , . . . , X n).
In order to find a link between identities of coalgebras and free coal gebras, we first define the latter. Free (coassociative) coalgebras (which more precisely should be called “cofree coalgebras”) were introduced by M. Sweedler in [9]. They are defined by the following universal property, which is dual to the universal property of tensor algebras.
