Thread: Field problem with factor ring

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.