About prime ideals in semirings of continuous function with values in unit segment

The properties of the prime ideals in semirings of the continuous functions on topological spaces with values in [0,1] are researches. Maximal ideals of the semirings of continuous [0,1]-valued functions are described. The characterizations of the compacts are received in terms of semiring of the functions. It is shown that the theory of ideals in considered semirings differs from the case of rings of continuous functions.