In this article we consider some relations between the topological properties of the spaces π and πππ(πΆ π (π)) with algebraic properties of πΆ π (π). We observe that the compactness of πππ(πΆ π (π)) is equivalent to the von-Neumann regularity of π π (π), the classical ring of quotients of πΆ π (π). Furthermore, we show that if π is a strongly zero-dimensional space, then each contraction of a minimal prime ideal of πΆ (π) is a minimal prime ideal of πΆ π (π) and in this case πππ(πΆ (π)) and πππ(πΆ π (π)) are homeomorphic spaces. We also observe that if π is an πΉ π -space, then πππ(πΆ π (π)) is compact if and only if π is countably basically disconnected if and only if πππ(πΆ π (π)) is homeomorphic with π½ 0 π. Finally, by introducing π§ β’ π -ideals, countably cozero complemented spaces, we obtain some conditions on π for which πππ(πΆ π (π)) becomes compact, basically disconnected and extremally disconnected.
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