The pointfree version of 𝓒 c (X) via the ranges of functions

IF 0.9 3区数学 Q2 MATHEMATICS Mathematica Slovaca Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0003

Maryam Taha, Ali Akbar Estaji, Maryam Robat Sarpoushi

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引用次数: 0

Abstract

Let R α := {r ∈ ℝ : coz(α − r) ≠ → p} for every α ∈ 𝓡(L). The ring 𝓒 c (L) is introduced as a pointfree version of the subring 𝓒 c (X) of C(X) by R α . In this paper, we show that 𝓒 c (X) is a z-good ring and every radical ideal in it is an absolutely convex ideal. Also, we study this result which for any frame L, there exists a zero-dimensional frame M, which is a continuous image of L and 𝓒 c (L) ≅ 𝓒 c (M).

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通过函数范围得到的𝓒 c (X) 的无点版本

让 R α := {r ∈ ℝ : coz(α - r) ≠ → p} 为每一个 α ∈ 𝓡(L) 的 R α :={r∈ℝ : coz(α - r) ≠ → p}。环 𝓒 c (L) 是作为 C(X) 的子环 𝓒 c (X) 的无点版本由 R α 引入的。在本文中，我们证明了𝓒 c (X) 是一个 z 好环，并且其中的每个根理想都是绝对凸理想。此外，我们还研究了这样一个结果，即对于任意框架 L，存在一个零维框架 M，它是 L 的连续映像，且 𝓒 c (L) ≅ 𝓒 c (M)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.

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