Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 17 1 2022 07 01 On some properties of the space of minimal prime ideals of 𝐶𝑐 (𝑋) 85 100 102622 10.52547/cgasa.2022.102622 EN Zahra Keshtkar Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Rostam Mohamadian Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Mehrdad Namdari Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Maryam Zeinali Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. Journal Article 2022 08 08 In this article we consider some relations between the topological properties of the spaces X and  Min(C_c (X)) with algebraic properties of C_c (X). We observe that the compactness of  Min(C_c (X)) is equivalent to the von-Neumann regularity of  q_c (X), the classical ring of quotients of C_c (X). Furthermore, we show that if 𝑋 is a strongly zero-dimensional space, then each contraction of a minimal prime ideal of 𝐶(𝑋) is a minimal prime ideal of C_c(X) and in this case 𝑀𝑖𝑛(𝐶(𝑋)) and Min(C_c (X)) are homeomorphic spaces. We also observe that if 𝑋 is an F_c-space, then  Min(C_c (X)) is compact if and only if 𝑋 is countably basically disconnected if and only if Min(C_c(X)) is homeomorphic with β₀X. Finally, by introducing z^o_c-ideals, countably cozero complemented spaces, we obtain some conditions on X for which  Min(C_c (X)) becomes compact, basically disconnected and extremally disconnected. https://cgasa.sbu.ac.ir/article_102622_fabfade2e239fe905af15ccfebc0a21e.pdf