Ideals of the Gaussian Integers
Given the Gaussian Integers
Then I am trying to show that
1) is an ideal in but is not maximal. To be clear, I mean 5 divides a, and 5 divides b.
To show it's an ideal, I have to show that it "absorbs" any element from Z[i] "into"
it... seems like something that should follow from number theory. Also, I am not sure how it is not maximal! I need to find some other ideal that I is properly contained in? I can't think of any!
2) is NOT a prime ideal in (<> refers to the principal ideal)...
and then I am trying to figure out how many elements there are in the factor ring
Any guidance or assistance appreciated! Thanks!!