We start by assuming that there is an involution on the coefficients, say .
By relabelling the knowns and unknowns if necessary, let us suppose that
Let us also suppose that there is an injective map from to and an injective map from to where and .
We now make the assumption which corresponds to the problem involving the algebra with involution:
If the mathematical problem we are trying to investigate involves elements of an algebra with involution, say , and we substitute for and for for and for , thenThere is a unique operation from to such that the following four conditions hold: