associated prime ideals in c(x)

the minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of c(x). the necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) i is an intersection of o , s, when x is basically disconnected. (iii) i=o , when x x has a countable base of neighborhoods. (iv) i is finitely generated. (v) / is countably generated, when x is compact and countable of first kind