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:
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!