布尔环及其谱的一些性质  

Some properties of Boolean rings and their sprctrum

作　　者：郭俊辉 GUO Jun-hui(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2022年第3期48-54,共7页Journal of Guangzhou University:Natural Science Edition

摘　　要：布尔环的来源背景是布尔代数,是英国数学家Boole提出的数学模型,由于缺乏物理背景,它后来的进展一度缓慢,直到Stone提出著名的斯通定理才得以继续发展。文章主要以一个简单的阐述语言去推演斯通定理,得益于在推演过程中对布尔环及其谱空间的了解,然后在布尔环上推广一个交换环的性质,并发现了布尔环谱空间的一些特殊的拓扑性质。The origin background of Boolean ring is Boolean algebra, a mathematical model proposed by British mathematician Boole. Due to the lack of physical background, its progress was slow until Stone put forward the famous Stone theorem to promote its development. In this paper, we try mainly to deduce Stone’s theorem by simple language, benefiting from the understanding of Boolean ring and its spectral space in the derivation process, the second part of this paper extends a property of commutative ring onto Boolean ring, and finds some special topological properties of the spectral space of Boolean ring.

关 键 词：布尔环 布尔代数 斯通定理 环的素谱 可构造拓扑 

分 类 号：O187.2[理学—数学]