Let

be the set of continous functions on the reals

It's not hard to show that it forms a ring under "pointwise" addition and multiplication:

Now, Let

I am trying to

i) Show that

is an ideal in

.

ii) Describe T/I using the 1st isomorphism theorem.

Well, in i), I think that if we let

then

so

so it's an ideal? Also, it contains the 0 element and is closed under "subtraction".

and in ii), I need to think of a ring homomorphism from

to some ring which has

as the kernel, but I can't seem to think what that would be!!

Any help appreciated.... and if anyone could verify my reasoning in (i) that would be great!

Thanks!!