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References
Bourbaki, N.: Algèbre commutative. chapt. I. Paris: Hermann 1961.
Cartan, H., Eilenberg, S.: Homological Algebra. Princeton: Princeton University Press 1956.
Gabriel, P., Popescu, N.: Caractérisation des catégories abeliennes avec générateurs et limites inductives exactes. C. Rend. Acad. Sci. Paris,258, 4188–4190 (1964).
Grothendieck, A.: Sur quelques points d'algèbre homologique. Tôhoku Math. J.9, 119–221 (1957).
Lazard, D.: Sur les modules plats. C. R. Acad. Sci. Paris,258, 6313–6316 (1964).
Matlis, E.: Cotorsion modules. Mem. Amer. Math. Soc.49, 1964.
Oberst, U., Röhrl, H.: Flat and coherent functors. J. of Algebra14, 91–105 (1970).
Richmann, F., Walker, E.: Primary abelian groups as modules over their endomorphism rings. Math. Z.89, 77–81 (1965).
Rotman, J.: A completion functor on modules and algebras. J. of Algebra9, 369–387 (1968).
Takeuchi, M.: A simple proof of Gabriel and Popescu's theorem. J. of Algebra18, 112–113 (1971).
Ulmer, F.: A categorical proof of the Gabriel-Popescu theorem. Mimeographed notes. Univ. of Zürich, 1969.
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Ulmer, F. A flatness criterion in Grothendieck categories. Invent Math 19, 331–336 (1973). https://doi.org/10.1007/BF01425418
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DOI: https://doi.org/10.1007/BF01425418