(ON THE COLOCALLY SOCLE OF C(X

(Let $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$ We introduce and study the concept of colocally socle of $C(X)$ as $C_{\mu}{S_{\lambda}}(X)=\left\{ f\in C(X): |X\backslash {S}^{\lambda}_{f}| \mu \right\}$, where ${{S}^{\lambda}_{f}}$ is the union of all open subsets $U$ in $X$ such that $|U\backslash Z(f)| \lambda$. $C_{\mu}{S_{\lambda}}(X)$ is a $z$-ideal of $C(X)$ containing ${{C}_{F}}(X)$. In particular $C_{{\aleph}_0}{S_{{\aleph}_0}}(X)=CC_F(X)$ is investigated. We characterize spaces $X$ for which the equality in the relation ${{C}_{F}}(X)\subseteq CC_F(X)\subseteq C(X)$ is hold. We determine the conditions such that $CC_F(X)$ is not prime in any subrings of $C(X)$ which contains the idempotents of $X$. The primness of $CC_F(X)$ in some subrings of $C(X)$ is investigated.