Show that is a field.
My proof so far:
Now,
Now, [tex](1+<x^2+1>)[tex] is the unity of
But I have trouble trying to prove every element has a unit.
Let be in
I need to find the inverse.
little help, please?
Thank you
It happens to be isomorphic to just in case you are interested.
Did you do the following theorems?
1.Given a commutative ring (with unity) and a maximal ideal then is a field.
2.If is a non-constant polynomial which is irreducible over the field then is a maximal ideal of .
So it remains to show that is irreducible over which it is because it is a degree 2 polynomials with no real zeros.