- #1
S_Manifesto
- 6
- 0
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.
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.