University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 11 1 2000 03 01 ASSOCIATED PRIME IDEALS IN C(X) - 31304 EN Journal Article 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 https://jsciences.ut.ac.ir/article_31304_4d0b33b5012968d7184664859cf30a80.pdf