2018/04/06 by Abolfazl Tarizadeh, Tarizadeh, Abolfazl
Mathematics · #13C10 #13C11 #13E99 #19A13 #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.1804.03007
openalex publication_date 2018/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a finitely many minimal primes or a finitely many maximal ideals then every finitely generated flat module over it is projective. It is also shown that if a particular subset of the prime spectrum of a ring satisfies some certain ascending or descending chain conditions then every finitely generated flat module over this ring is projective. These results generalize some major results in the literature on the projectivity of finitely generated flat modules.