Rings whose finitely generated torsion modules in the sense of Dickson decompose into direct sums of cyclic submodules

Alberto Facchini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1980)

  • Volume: 68, Issue: 1, page 13-21
  • ISSN: 0392-7881

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Facchini, Alberto. "Rings whose finitely generated torsion modules in the sense of Dickson decompose into direct sums of cyclic submodules." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 68.1 (1980): 13-21. <http://eudml.org/doc/288762>.

@article{Facchini1980,
author = {Facchini, Alberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {1},
number = {1},
pages = {13-21},
publisher = {Accademia Nazionale dei Lincei},
title = {Rings whose finitely generated torsion modules in the sense of Dickson decompose into direct sums of cyclic submodules},
url = {http://eudml.org/doc/288762},
volume = {68},
year = {1980},
}

TY - JOUR
AU - Facchini, Alberto
TI - Rings whose finitely generated torsion modules in the sense of Dickson decompose into direct sums of cyclic submodules
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1980/1//
PB - Accademia Nazionale dei Lincei
VL - 68
IS - 1
SP - 13
EP - 21
LA - eng
UR - http://eudml.org/doc/288762
ER -

References

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  2. Dickson, S.E. (1968) - Decomposition of modules. II. Rings without chain conditions, «Math. Z.», 104, 349-357. Zbl0164.34703MR229678
  3. Facchini, A. (1979) - Reflexive rings, «Symposia Math.», XXIII, 415-449. MR565614
  4. Facchini, A. (1980) - On the ring of quotients of a Noetherian commutative ring with respect to the Dickson topology, «Rend. Sem. Mat. Univ. Padova», 62. Zbl0441.13006MR582953
  5. Fine, N.J., Gillman, L. and Lambek, J. (1965) - Rings of quotients of rings of functions, McGill Univ. Press. Zbl0143.35704MR200747
  6. Kaplansky, I. (1952) - Modules over Dedekind rings and valuation rings, «Trans. Am. Math. Soc.», 72, 327-340. Zbl0046.25701MR46349
  7. Matlis, E. (1968) - Reflexive domains, «J. Algebra», 8, 1-33. MR220713
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  9. Menini, C., Orsatti, A. (1979) - Duality over a quasi-injective module and commutative ℱ -reflexive rings, «Symposia Math.», XXIII, 145-179. Zbl0429.13004MR565604
  10. Sharpe, D.W. and Vamos, P. (1972) - Injective modules, Cambridge Univ. Press. Zbl0245.13001MR360706
  11. Shores, T.S. (1971) - Decompositions of finitely generated modules, «Proc. Am. Math. Soc.», 30, 445-450. Zbl0203.05002MR281708
  12. Shores, T.S. (1972) - The structure of Loewy modules, «J. reine und angew. Math.», 254, 204-220. Zbl0235.16024MR318231
  13. Shores, T.S. (1976) - A topological criterion for primary decomposition, «Acta Math. Ac. Sc. Hungaricae», 28, 383-387. Zbl0337.13002MR429863
  14. Shores, T.S. and Lewis, W.J. (1974) - Serial modules and endomorphism rings, «Duke Math. J.», 41, 889-909. Zbl0294.13007MR352079
  15. Stenström, B. (1970) - On the completion of modules in an additive topology, «J. Algebra», 16, 523-540. Zbl0206.32703MR271145
  16. Stenström, B. (1975) - Rings of Quotients, Springer-Verlag. MR389953

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