2019/10/22 by A. Tarizadeh, Tarizadeh, A., M. R. Rezaee +1
Mathematics · #13A15 #14A05 #14M27 #54A20 #54D35 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1910.09884
openalex publication_date 2019/10/22 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this paper, new advances on the compactifications of topological spaces, especially on the Stone-Čech and Alexandroff compactifications have been made. Among the main results, it is proved that the minimal spectrum of the direct product of a family of integral domains indexed by a set X is the Stone-Čech compactification of the discrete space X. Dually, it is proved that the maximal spectrum of the direct product of a family of local rings indexed by X is also the Stone-Čech compactification of the discrete space X. The Alexandroff (one-point) compactification of a discrete space is constructed by a new method. Next, we proceed to give a natural and quite simple way to construct ultra-rings. Then this new approach is used to obtain several new results on the Stone-Čech compactification.