Note on the transitivity of pure essential extensions

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Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 U.S.A.
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy

[B] N. Bourbaki, Algèbre commutative, Chap. 1-2, Hermann, Paris, 1961.
[Br] W. Brandal, Almost maximal integral domains and finitely generated modules, Trans. Amer. Math. Soc. 183 (1973), 203-222.
[F] L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, London, 1971.
[FS] L. Fuchs and L. Salce, Modules over Valuation Domains, Lecture Notes in Pure and Appl. Math. 97, Dekker, New York, 1985.
[GG] J. L. Gómez Pardo and P. A. Guil Asensio, Chain conditions on direct summands and pure quotient modules, preprint.
[GJ] L. Gruson et C. U. Jensen, Modules algébriquement compacts et foncteurs $lim \in d^{(i)}$ , C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1651-A1653.
[K] R. Kiełpiński, On Γ-pure-injective modules, Bull. Acad. Pol. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 127-131.
[M] J. M. Maranda, On pure subgroups of abelian groups, Arch. Math. (Basel) 11 (1960), 1-13.
[S] B. T. Stenström, Pure submodules, Ark. Mat. 7 (1967), 159-171.
[W] R. B. Warfield, Jr., Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719.