Let $mathcal{R}L$ be the ring of real-valued continuous functions on a frame $L$. The aim of this paper is to study the relation between minimality of ideals $I$ of $mathcal{R}L$ and the set of all zero sets in $L$ determined by elements of $I$. To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame $L$, it is proved that the $f$-ring $mathcal{R}L$ is isomorphic to the $f$-ring $ C(Sigma L)$ of all real continuous functions on the topological space $Sigma L$. Finally, a one-one correspondence is presented between the set of isolated points of $Sigma L$ and the set of atoms of $L$.
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机译：令$ mathcal {R} L $为框架$ L $上的实值连续函数的环。本文的目的是研究$ mathcal {R} L $的理想$ I $的极小值与$ I $元素确定的$ L $中所有零集的集合之间的关系。为此，引入了coz不相交，coz空间和coz密度的概念。在coz密集框架$ L $的情况下，证明了$ f $环$ mathcal {R} L $与所有$ f $环$ C（ Sigma L）$同构拓扑空间$ Sigma L $上的实连续函数。最后，在$ Sigma L $的孤立点集合与$ L $的原子集合之间呈现一一对应关系。
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