Geodesic
A Module is Flat if and Only if its Character Module isInjective
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 237-243

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The purpose of this expository note is to establish the fact mentioned inthe title. While this is not difficult and requires no new ideas, it seemsworth doing, as such a simple characterization does not appear explicitly ina recent treatise on the subject of flat modules [Bourbaki XXVII, Chapter1]. 
Lambek, J. A Module is Flat if and Only if its Character Module isInjective. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 237-243. doi: 10.4153/CMB-1964-021-9
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     title = {A {Module} is {Flat} if and {Only} if its {Character} {Module} {isInjective}},
     journal = {Canadian mathematical bulletin},
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