153
Views
16
CrossRef citations to date
0
Altmetric
Miscellany

Multiplication Modules in Which Every Prime Submodule is Contained in a Unique Maximal Submodule

, &
Pages 1945-1959 | Received 01 Nov 2002, Published online: 21 Oct 2011

References

  • Abd El-Bast , Z. and Smith , P. F. 1988 . Multiplication modules . Comm. Algebra , 16 ( 4 ) : 755 – 779 .
  • Anderson , D. D. 2000 . Some remarks on multiplication ideals, II . Comm. Algebra , 28 ( 5 ) : 2577 – 2583 .
  • Anderson , D. D. and AI-Shaniafi , Y. 2002 . Multiplication modules and the ideal θ(M) . Comm. Algebra , 30 ( 7 ) : 3383 – 3390 . [CROSSREF]
  • Anderson , D. D. and Camillo , V. P. 2002 . Commutative rings whose elements are a sum of a unit and idempotent . Comm. Algebra , 30 ( 7 ) : 3327 – 3336 . [CROSSREF]
  • Anderson , F. W. and Fuller , K. R. 1974 . Rings and Categories of Modules New York : Springer-Verlag .
  • Belluce , L. P. 1991 . Spectral spaces and non-commutative rings . Comm. Algebra , 19 ( 7 ) : 1855 – 1865 .
  • Belluce , L. P. 1997 . Spectral closure for noncommutative rings . Comm. Algebra , 25 ( 5 ) : 1513 – 1536 .
  • Demarco , G. and Orsatti , A. 1971 . Commutative rings in which every prime ideal is contained in a unique maximal ideal . Proc. Amer. Math. Soc. , 30 ( 3 ) : 459 – 466 .
  • Kelley , J. P. 1955 . General Topology New York : Springer-Verlag .
  • Koh , K. 1972 . On a representation of a strongly harmonic ring by Sheaves . Pacific J. Math. , 41 ( 2 ) : 459 – 468 .
  • Low , G. M. and Smith , P. F. 1990 . Multiplication modules and ideals . Comm. Algebra , 18 ( 12 ) : 4353 – 4375 .
  • Lu , C. P. 1995 . Spectra of modules . Comm. Algebra , 23 ( 10 ) : 3741 – 3752 .
  • McCasland , R. L. , Moore , M. E. and Smith , P. F. 1997 . On the spectrum of a module over a commutative ring . Comm. Algebra , 25 ( 1 ) : 79 – 103 .
  • Moore , M. E. and Smith , S. J. 2002 . Prime and radical submodules of modules over commutative rings . Comm. Algebra , 30 ( 10 ) : 5037 – 5064 . [CROSSREF]
  • Simmons , H. 1980 . Reticulated rings . J. Algebra , 66 : 169 – 192 .
  • Smith , W. W. 1969 . Projective ideals of finite type . Canad. J. Math. , 21 : 1057 – 1061 .
  • Smith , P. F. 1988 . Some remarks on multiplication modules . Arch. Math. (Basel) , 50 : 223 – 235 .
  • Sun , S. H. 1991 . Noncommutative rings in which every prime ideal is contained in a unique maximal ideal . J. Pure Appl. Algebra , 76 : 179 – 192 . [CROSSREF]
  • Zariski , O. and Samuel , P. 1960 . Commutative Algebra New York : Springer-Verlag .
  • Zhang , G. 1999 . Spectra of modules over any ring . J. Nanjing Univ. Math. Biquarterly , 16 ( 1 ) : 42 – 52 .
  • Zhang , G. and Tong , W. 2000 . Spectral spaces of top right R-modules . J. Nanjing Univ. Math. Biquarterly , 17 ( 1 ) : 26 – 33 .
  • #Communicated by I. Swanson.

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:

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:

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.