Originally Posted by

**andreas** Hello I want to solve the following problem:

Let R = **Z**( $\displaystyle sqrt2$** ) = **{ a+b$\displaystyle sqrt2$|a,b belong to **Z.**

*2.* If **I **= ($\displaystyle sqrt 2 $) is the ideal generated by $\displaystyle sqrt(2)$, prove that R/I~=**Z2** (~= means isomorphic).

In *2. *I understood **I **as all elements of **R **multiplied by $\displaystyle sqrt(2)$) . Am I correct?

How shall I prove isomorphism? I tried the following function from **R **to **Z****2: **f(a+$\displaystyle sqrt2$b+**I**)= a mod 2. But it is only hommomorphism in my opinion, not isomorphism.