Geodesic
When is the category of flat modules abelian?
Fundamenta Mathematicae, Tome 147 (1995) no. 1, pp. 83-91

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Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R. 
J. García; J. Martínez Hernández. When is the category of flat modules abelian?. Fundamenta Mathematicae, Tome 147 (1995) no. 1, pp. 83-91. doi: 10.4064/fm-147-1-83-91
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