Notes on finitely generated flat modules
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 419-427
https://doi.org/10.4134/BKMS.b190294
Published online March 31, 2020
Abolfazl Tarizadeh
University of Maragheh
Abstract : In this paper, 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 finitely many minimal primes or 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.
Keywords : Flat module, flat topology, patch topology, projectivity, S-ring
MSC numbers : 13C10, 19A13, 13C11, 13E99
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