# On the projectivity of finitely generated flat modules

## TL;DR

This paper investigates conditions under which finitely generated flat modules over commutative rings are projective, extending previous results by analyzing exterior powers and invariant factors.

## Contribution

It generalizes existing results on the projectivity of finitely generated flat modules using exterior powers and invariant factors.

## Key findings

- New criteria for projectivity of finitely generated flat modules
- Generalizations of prior results by Endo, Vasconcelos, and others
- Enhanced understanding of module structure over commutative rings

## Abstract

In this paper, the projectivity of a finitely generated flat module of a commutative ring is studied through its exterior powers and invariant factors and then various new results are obtained. Specially, the related results of Endo, Vasconcelos, Wiegand, Cox-Rush and Puninski-Rothmaler on the projectivity of finitely generated flat modules are generalized.