Note on the transitivity of pure essential extensions

Laszlo Fuchs; Luigi Salce; Paolo Zanardo

Colloquium Mathematicae (1998)

  • Volume: 78, Issue: 2, page 283-291
  • ISSN: 0010-1354

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Fuchs, Laszlo, Salce, Luigi, and Zanardo, Paolo. "Note on the transitivity of pure essential extensions." Colloquium Mathematicae 78.2 (1998): 283-291. <http://eudml.org/doc/210615>.

@article{Fuchs1998,
author = {Fuchs, Laszlo, Salce, Luigi, Zanardo, Paolo},
journal = {Colloquium Mathematicae},
keywords = {pure submodule; relatively divisible submodule; pure-essential extension; RD-submodule; RD-essential extension; valuation domain},
language = {eng},
number = {2},
pages = {283-291},
title = {Note on the transitivity of pure essential extensions},
url = {http://eudml.org/doc/210615},
volume = {78},
year = {1998},
}

TY - JOUR
AU - Fuchs, Laszlo
AU - Salce, Luigi
AU - Zanardo, Paolo
TI - Note on the transitivity of pure essential extensions
JO - Colloquium Mathematicae
PY - 1998
VL - 78
IS - 2
SP - 283
EP - 291
LA - eng
KW - pure submodule; relatively divisible submodule; pure-essential extension; RD-submodule; RD-essential extension; valuation domain
UR - http://eudml.org/doc/210615
ER -

References

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  1. [B] N. Bourbaki, Algèbre commutative, Chap. 1-2, Hermann, Paris, 1961. Zbl0205.06001
  2. [Br] W. Brandal, Almost maximal integral domains and finitely generated modules, Trans. Amer. Math. Soc. 183 (1973), 203-222. Zbl0273.13011
  3. [F] L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, London, 1971. 
  4. [FS] L. Fuchs and L. Salce, Modules over Valuation Domains, Lecture Notes in Pure and Appl. Math. 97, Dekker, New York, 1985. Zbl0578.13004
  5. [GG] J. L. Gómez Pardo and P. A. Guil Asensio, Chain conditions on direct summands and pure quotient modules, preprint. 
  6. [GJ] L. Gruson et C. U. Jensen, Modules algébriquement compacts et foncteurs ( i ) , C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1651-A1653. Zbl0259.18015
  7. [K] R. Kiełpiński, On Γ-pure-injective modules, Bull. Acad. Pol. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 127-131. Zbl0159.04602
  8. [M] J. M. Maranda, On pure subgroups of abelian groups, Arch. Math. (Basel) 11 (1960), 1-13. Zbl0109.01701
  9. [S] B. T. Stenström, Pure submodules, Ark. Mat. 7 (1967), 159-171. Zbl0153.34302
  10. [W] R. B. Warfield, Jr., Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719. Zbl0172.04801

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