I must find an isomorphism between and .
The problem is that multiplication is defined entirely differently in the two rings. Any attempt by me to define an iso between the two breaks down at multiplication.
No. Just like multiplication on RxR = C isn't defined by (a,b)(c,d) = (ac, bd) but by (a,c)(b,d) = (ac-bd, ad+bc).Originally Posted by Treadstone 71
Define by , where is the unique representative of degree less than 2 of an element in . This is a bijection. Then define
, where the multiplication on the right is the one in . Then work out what this means in . Compare this to the formula for complex multiplication, and think about an explanation.
Hope this helps.