1) Show that (R,*,+) is a ring, where (x*y)=x+y+2 and (x+y)=2xy+4x+4y+6. Find the set of unit elements for the second operation. I understand that the Ring Axioms is 1. (R,+) is an albein group. 2. Multiplication is associative and 3. Multiplication distributes. I just don't understand how to go about this. A First Course in Abstract Algebra by John Fraleigh fails to show any examples of this type. 2) Let f: Z[√d]→M be an application such that f)x+y√d=A where [x y] A = Matrix[yd x] Show that f is an isomorphism of rings. I understand that I have to check the conditions of it being isomorphic, but once again the book does not give examples of how to do so. It's hard to attempt problems when I don't know where to begin.