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Original Articles

On the Countability of Noetherian Dimension of Modules

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Pages 4073-4083 | Received 01 Aug 2002, Accepted 01 Jan 2004, Published online: 24 Jun 2011

References

  • Albu , T. and Vamos , P. 1998 . “ Global Krull dimension and global dual Krull dimension of valuation rings, abelian groups, modules theory, and topology ” . In Proc. 37 – 54 . Marcel-Dekker .
  • Albu , T. and Smith , P. F. 1999 . Dual Krull dimension and duality . Rocky Mountain J. Math. , 29 : 1153 – 1164 .
  • Bass , H. 1971 . Descending chains and the Krull ordinal of commutative rings . J. Pure Appl. Algebra , 1 : 347 – 360 .
  • Brookfield , G. 2002 . The length of Noetherian modules . Comm. Algebra , 30 : 3177 – 3204 .
  • Chambless , L. 1980 . N-dimension and N-critical modules, application to Artinian modules . Comm. Algebra , 16 : 1561 – 1592 .
  • Fuchs , L. 1970 . Torsion preradical and ascending Loewy series of modules . J. Reine und Angew. Math. , 239 : 169 – 179 .
  • Goodearl , K. R. and Zimmermann-Huisgen , B. 1986 . Lengths of submodule chain versus Krull dimension in Non-Noetherian modules . Math. Z. , 191 : 519 – 527 .
  • Gordon , R. and Robson , J. C. 1973 . Krull dimension . Mem. Amer. Math. Soc. , 133
  • Gulliksen , T. H. 1973 . A theory of length for Noetherian modules . J. Pure Appl. Algebra , 3 : 159 – 170 .
  • Karamzadeh , O. A. S. 1974 . Noetherian-Dimension, Ph.D. thesis, Exeter, England
  • Karamzadeh , O. A. S. 1982 . When are Artinian modules countably generated? . Bull. Iran. Math. Soc. , 9 : 171 – 176 .
  • Karamzadeh , O. A. S. and Motamedi , M. 1994 . On α-Dicc modules . Comm. Algebra , 22 : 1933 – 1944 .
  • Karamzadeh , O. A. S. and Motamedi , M. 1995 . a-Noetherian and Artinian modules . Comm. Algebra , 23 : 3685 – 3703 .
  • Karamzadeh , O. A. S. and Sajedinejad , A. R. 2001 . Atomic modules . Comm. Algebra , 29 : 2757 – 2773 .
  • Karamzadeh , O. A. S. and Sajedinejad , A. R. 2002 . On the Loewy length and the Noetherian dimension of Artinian modules . Comm. Algebra , 30 : 1077 – 1084 .
  • Kirby , D. 1990 . Dimension and length for Artinian modules . Quart. J. Math. Oxford , 41 : 419 – 429 .
  • Krause , G. 1973 . Descending chains of submodules and the Krull dimension of Noetherian modules . J. Pure Appl. Algebra , 3 : 385 – 397 .
  • Lemonnier , B. 1972 . Deviation des ensembless et groupes totalement ordonnes . Bull. Sci. Math. , 96 : 289 – 303 .
  • Lemonnier , B. 1978 . Dimension de Krull et codeviation, application au theorem d'Eakin . Comm. Algebra , 6 : 1647 – 1665 .
  • Puczylowski , E. R. 1995 . On the uniform dimension of the radical of a module . Comm. Algebra , 23 : 771 – 776 .
  • Roberts , R. N. 1975 . Krull dimension for Artinian modules over quasi local commutative rings . Quart. J. Math. Oxford , 26 : 269 – 273 .
  • Sharp , R. Y. 1989 . “ A method for the study of Artinian modules with an application to asymptotic behavior ” . In Commutative Algebra , Math. Sci. Res. Inst. Pub 10, 15 443 – 465 . New York : Springer . (Berkeley, CA, 1987)
  • Vamos , P. 1969 . The dual of the notion of finitely generated . J. Lon. Math. Soc. , 43 : 642 – 646 .
  • #Communicated by B. Huisgen-Zimmermann.

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