2016/12/17 by Abolfazl Tarizadeh, Tarizadeh, Abolfazl
Computer Science · Mathematics · #03E10 #13A99 #13C10 #19A13 #Commutative Algebra (math.AC) #Computability, Logic, AI Algorithms #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1612.05745
openalex publication_date 2016/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, first we obtain some new and interesting results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally of finite type projective module is continuous with respect to the upper topology (by contract, it is well known this map is not necessarily continuous with respect to the discrete topology). It is also proved that a finitely generated flat module is projective if and only if its rank map is continuous with respect to the upper topology.