Sentence:  This motivates a generalization, and exponential <WSD>homomorphisms</WSD> are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates. 
Meaning of the word marked with <WSD> tags:  A structure-preserving (map) between two algebraic structures of the same type, such as (groups), (rings), or vector spaces.