Ring of continuous functions, prime ideals, maximal ideals, zero sets.
Abstract
It is well known that the set C[0, 1] of real-valuedcontinuous functions on the closed interval [0, 1]has a natural ring structure. Its maximal idealsare known to be points. Here we show thatalthough there exist prime ideals which are notmaximal, the zero set is again a singleton. In particular,each prime ideal is contained in a uniquemaximal ideal.
