Let $C(\mathbb R)$ denote the ring of all continuous real-valued functions on $\mathbb R$, with the operations of pointwise addition and pointwise multiplication. Which of the following form an ideal in this ring?
a. The set of all $C^\infty$ functions with compact support.
b. The set of all continuous functions with compact support.
c. The set of all continuous functions which vanish at infinity, i.e. functions $f$ such that $\displaystyle\lim_{ x\to\infty} f(x) = 0$.
Please somebody help how can I solve this problem. I have no idea.