Answer to Question #15229 in Abstract Algebra for abadhutamla

Question

Let C(R) denote the ring of all continuous real-valued functions on
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^infinity functions with compact support.
b. The set of all continuous functions with compact support.
c. The set of all continuous functions which vanish at innity, i.e. functions
f such that lim x tends to infinity f(x) = 0