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مقالات فارسیISIکنفرانسهاژورنالها

On some properties of the space of minimal prime ideals of 𝐶𝑐 (𝑋)

محل انتشار: مجله نظریه رسته ها و ساختارهای کلی جبری با کاربردها، دوره: 17، شماره: 1
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 251

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لینک ثابت به این مقاله:
https://civilica.com/doc/1503824

شناسه ملی سند علمی:

JR_CGASAT-17-1_003

تاریخ نمایه سازی: 1 شهریور 1401

چکیده مقاله:

In this article we consider some relations between the topological properties of the spaces X and  Min(Cc (X)) with algebraic properties of Cc (X). We observe that the compactness of  Min(Cc (X)) is equivalent to the von-Neumann regularity of  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 𝐶(𝑋) is a minimal prime ideal of Cc(X) and in this case 𝑀𝑖𝑛(𝐶(𝑋)) and Min(Cc (X)) are homeomorphic spaces. We also observe that if 𝑋 is an Fc-space, then  Min(Cc (X)) is compact if and only if 𝑋 is countably basically disconnected if and only if Min(Cc(X)) is homeomorphic with β۰X. Finally, by introducing zoc-ideals, countably cozero complemented spaces, we obtain some conditions on X for which  Min(Cc (X)) becomes compact, basically disconnected and extremally disconnected.

کلیدواژه ها:

The space of minimal prime ideals ، strongly zero-dimensional space ، countably basically disconnected space ، countably cozero complemented space ، z^۰_c-ideals

نویسندگان

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.

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