# Answer to Question #15229 in Abstract Algebra for abadhutamla

Question #15229

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 innity, i.e. functions

f such that lim x tends to infinity f(x) = 0

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 innity, i.e. functions

f such that lim x tends to infinity f(x) = 0

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