2015/03/14 by Abolfazl Tarizadeh, Tarizadeh, Abolfazl
Mathematics · #13A99 #13B10 #13C11 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1503.04299
openalex publication_date 2015/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, a new and natural topology on the prime spectrum is established which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also some sophisticated properties of the flat topology are proved. Specially, various algebraic characterizations for the noetherianness of the flat topology are given. Using the flat topology, then some facts on the structure of the prime ideals of a ring come to light which are not in the access of the Zariski topology.