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## Main Question or Discussion Point

Someone, please help me solve this problem:

First if R is a ring and * is an involution, then U(R, *):= {x \in R|x* · x = 1}

(an involution * is an antihomomorphism such that a** = a for any a)

Now the problem. Find two rings (R, S) with involutions (*, ^) such that U(R, *) is homomorphic to (S, ^). and R and S are not homomorphic.

My first problem is that i do not know of any involutions except for conjugation and transposition for matrixes.

First if R is a ring and * is an involution, then U(R, *):= {x \in R|x* · x = 1}

(an involution * is an antihomomorphism such that a** = a for any a)

Now the problem. Find two rings (R, S) with involutions (*, ^) such that U(R, *) is homomorphic to (S, ^). and R and S are not homomorphic.

My first problem is that i do not know of any involutions except for conjugation and transposition for matrixes.