ATOMIC MODULES

REFERENCES

• Albu , T. and Smith , P. F. 1995 . “ Duall Relative Krull Dimension of Modules over Commutative Rings ” . In Abelian Groups and Modules Edited by: Facchini , A. and Menini , C. 1 – 15 . Kluwer .
   Google Scholar
• Albu , T. and Smith , P. F. 1977 . Localization of Modular Lattices Krull Dimension, and the Hopkins–Levitzki Theorem (II) . Comm. Algebra , 25 : 111 – 1128 .
   Google Scholar
• Chambless , L. N. 1980 . N-dimension and N-critical Modules. Application to Artinian Modules . Comm. Algebra , 8 : 1561 – 1592 .
   Web of Science ®Google Scholar
• Facchini , A. , Herbera , D. , Levy , L. S. and Vamos , P. 1995 . Krull–Schmidt Fails for Artinian Modules . Proc. Amer. Math. Soc. , 123 : 3587 – 3600 .
   Web of Science ®Google Scholar
• Goodearl , K. R. and Warfield , R. B. JR. 1989 . An Introduction to Non-Commutative Noetherian Rings Cambridge Univ. Press .
   Google Scholar
• Gordon , R. and Robson , J. C. 1973 . Krull-dimension . Mem. Amer. Math. Soc. , 133
   Google Scholar
• Heinzer , W. and Lantz , D. 1985 . Artinian Modules and Modules of Which All Proper Submodules are Finitely Generated . J. Algebra , 95 : 201 – 216 .
   Web of Science ®Google Scholar
• Huang , I. C. 1995 . Constructions of Artinian Modules . Comm. Algebra , : 5025 – 5030 .
   Web of Science ®Google Scholar
• Jategaonkar , A. V. 1986 . Localization in Noetherian rings Cambridge. Univ. Press .
   Google Scholar
• Karamzadeh , O. A.S. 1974 . Noetherian Dimension , Ph.D. Thesis Exeter .
   Google Scholar
• Karamzadeh , O. A.S. and Motamedi , M. 1994 . On α-Dicc Modules . Comm. Algebra , 22 : 1933 – 1944 .
   Web of Science ®Google Scholar
• Karamzadeh , O. A.S. and Motamedi , M. 1995 . α-Noetherian and Artinian Modules . Comm. Algebra , 23 : 3685 – 3703 .
   Web of Science ®Google Scholar
• Karamzadeh , O. A.S. and Sajedinejad , A. R. On the Lowey Length and The Noetherian Dimension of Artinian Modules . Comm. Algebra , (to appear)
   Google Scholar
• Kirby , D. 1990 . Dimension and Length for Arlinian Modules . Quart. J. Math. Oxford , 41 : 419 – 429 .
   Web of Science ®Google Scholar
• Krause , G. 1972 . On the Krull-Dimension of Left Noetherian Rings . J. Algebra , 23 : 88 – 99 .
   Web of Science ®Google Scholar
• Lemonnier , B. 1972 . Deviation des Ensembless et Groupes Abeliens Totalement Ordomnes . Bull. Sci. Math. , 96 : 289 – 303 .
   Google Scholar
• Lemonnier , B. 1978 . Dimension de Krull et codeviation. Application au theorem d'Eakin . Comm. Algebra , 16 : 1647 – 1665 .
   Web of Science ®Google Scholar
• Matlis , E. 1960 . Modules with Descending Chain Conditions . Trans. Amer. Math. Soc. , 97 : 495 – 508 .
   Google Scholar
• McConnell , J. C. and Robson , J. C. 1987 . Noncommutative Noetherian Rings New York : Wiley-interscience .
   Google Scholar
• Northcott , D. G. 1974 . Injective envelopes and inverse polynomials . J. Lon. Math. Soc. , 8 : 290 – 296 .
   Web of Science ®Google Scholar
• Roberts , R. N. 1975 . Krull Dimension for Artinian Modules over Quasi Local Commutative rings . Quart. J. Math. Oxford , 26 : 269 – 273 .
   Web of Science ®Google Scholar
• Sharp , R. Y. 1989 . A Method for the study of Artinian modules with an application to asymptotic behavior, Proceeding of micr-program (Commutative Algebra) 443 – 464 . Springer-Verlag .
   Google Scholar
• Vamos , P. 1969 . The Dual of the Notion of Finitely Generated . J. Lon. Math. Soc. , 43 : 642 – 646 .
   Web of Science ®Google Scholar
• Weakley , W. D. 1983 . Modules whose Proper Submodules are Finitely Generated . J. Algebra , 84 : 189 – 219 .
   Web of Science ®Google Scholar
• Wisbauer , R. Foundations of Module and Ring Theory Vol. 991 , Reading : Gordon and Breach .
   Google Scholar