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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Abstract Algebra: Rings, Unit Elements, Fields

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