%0 Journal Article %T On some properties of the space of minimal prime ideals of 𝐢𝑐 (𝑋) %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Keshtkar, Zahra %A Mohamadian, Rostam %A Namdari, Mehrdad %A Zeinali, Maryam %D 2022 %\ 07/01/2022 %V 17 %N 1 %P 85-100 %! On some properties of the space of minimal prime ideals of 𝐢𝑐 (𝑋) %K The space of minimal prime ideals %K strongly zero-dimensional space %K countably basically disconnected space %K countably cozero complemented space %K $z^0_c$-ideals %R 10.52547/cgasa.2022.102622 %X In this article we consider some relations between the topological properties of the spaces X and Β Min(Cc (X)) with algebraic properties of Cc (X). We observe that the compactness of Β Min(Cc (X)) is equivalent to the von-Neumann regularity ofΒ  qc (X), the classical ring of quotients of Cc (X). Furthermore, we show that if 𝑋 is a strongly zero-dimensional space, then each contraction of a minimal prime ideal of 𝐢(𝑋) is a minimal prime ideal of Cc(X) and in this case 𝑀𝑖𝑛(𝐢(𝑋)) and Min(Cc (X)) are homeomorphic spaces. We also observe that if 𝑋 is an Fc-space, thenΒ  Min(Cc (X)) is compact if and only if 𝑋 is countably basically disconnected if and only if Min(Cc(X)) is homeomorphic with Ξ²0X. Finally, by introducing zoc-ideals, countably cozero complemented spaces, we obtain some conditions on X for which Β Min(Cc (X)) becomes compact, basically disconnected and extremally disconnected. %U https://cgasa.sbu.ac.ir/article_102622_fabfade2e239fe905af15ccfebc0a21e.pdf