- #1
Mechmathian
- 35
- 0
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.