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Abolfazl Tarizadeh

Abolfazl Tarizadeh

Academic rank: Associate Professor
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Education: PhD.
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Faculty: Faculty of Basic Sciences
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Research

Title
Notes on finitely generated flat modules
Type
JournalPaper
Keywords
flat module; flat topology; patch topology; projectivity; S-ring
Year
2020
Journal Bulletin of the Korean Mathematical Society
DOI
Researchers Abolfazl Tarizadeh

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.