Advanced search
Publication Cover
Communications in Algebra Volume 31, 2003 - Issue 7
Submit an article Journal homepage
85
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Modules with RD-Composition Series over a Commutative Ring

François Couchot Department of Mathematics, Universite de Caen, Caen Cedex, France; Department of Mathematics, Universite de Caen, B.P. 5186-Campus II-Sciences 3, 14 032, Caen Cedex 5, FranceCorrespondence[email protected] [email protected]
Pages 3171-3194 | Received 01 Jul 2001, Published online: 31 Aug 2006

References

  • Fuchs , L. and Salce , L. 1983 . Uniserial modules over valuation rings . J. Algebra , 85 : 14 – 31 .
  • Fuchs , L. and Salce , L. 1985 . Modules Over Valuation Domains , Lecture Notes in Pure and Appl. Math. Vol. 97 , New York : Marcel Dekker .
  • Henriksen , M. 1955–56 . Some remarks on elementary divisor rings II . Michigan Math. J. , 3 : 159 – 163 .
  • Kaplansky , I. 1949 . Elementary divisors and modules . Trans. Amer. Math. Soc. , 66 : 464 – 491 .
  • Lambek , J. 1966 . Lectures on Rings and Modules Waltham : Blaisdell .
  • Larsen , M. D. , Lewis , W. J. and Shores , T. S. 1974 . Elementary divisor ring and finitely presented modules . Trans. Amer. Math. Soc. , 187 : 231 – 248 .
  • Mathis , E. 1958 . Injective modules over Noetherian rings . Pac. J. Math. , 8 : 511 – 528 .
  • Mathis , E. 1964 . Cotorsion modules . Mem. Amer. Math. Soc. , : 49
  • Naudé , C. 1985 . A note on polycyclic modules over Bézout domains . Comm. Algebra , 13 ( 10 ) : 2211 – 2217 .
  • Naudé , C. G. , Naude , G. and Pretorius , L. M. 1986 . Equational characterizations of relative injectivities . Comm. Algebra , 14 ( 1 ) : 39 – 49 .
  • Pierce , R. S. 1967 . Modules over commutative regular rings . Mem. Amer. Math. Soc. , : 70
  • Quentel , Y. 1971 . Sur la compacité du spectre minimal d'un anneau . Bull. Soc. Math. France , 99 : 265 – 272 .
  • Salce , L. and Zanardo , P. 1984 . Finitely generated modules over valuation rings . Comm. Algebra , 12 : 1795 – 1812 .
  • Shores , T. S. and Wiegand , R. 1974 . Rings whose finitely generated modules are direct sums of cyclics . J. Algebra , 32 : 152 – 172 .
  • Vámos , P. 1977 . The decomposition of finitely generated modules and fractionnally self-injective rings . J. London Math. Soc. , 16 ( 2 ) : 209 – 220 .
  • Warfield , R. B. 1969 . Purity and algebraic compactness for modules . Pac. J. Math. , 28 ( 3 ) : 689 – 719 .
  • Warfield , R. B. 1970 . Decomposability of finitely presented modules . Proc. Amer. Math. Soc. , 25 : 167 – 172 .
  • Wiegand , R. 1978 . Rings of Bounded Module Type , LNM 700 143 – 150 .
  • Wiegand , R. and Wiegand , S. 1977 . Commutative Rings Whose Finitely Generated Modules are Direct Sum of Cyclics , LNM Vol. 616 , 406 – 423 . Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.