Advanced search
Publication Cover
Communications in Algebra Volume 38, 2010 - Issue 10
Submit an article Journal homepage
76
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On the Catenaricity of Noetherian Local Rings and Quasi Unmixed Artinian Modules

Le Thanh Nhan Thai Nguyen College of Sciences, Thai Nguyen, VietnamCorrespondence[email protected]
&
Tran Nguyen An Thai Nguyen College of Education, Thai Nguyen, Vietnam
Pages 3728-3736 | Received 02 Mar 2009, Published online: 24 Nov 2010

REFERENCES

  • Brodmann , M. ( 1978 ). A particular class of regular domains . J. Algebra 54 : 366 – 373 .
  • Brodmann , M. , Rotthaus , C. ( 1983 ). A peculiar unmixed domain . Proc. AMS. 87 : 596 – 600 .
  • Brodmann , M. , Sharp , R. Y. ( 1998 ). Local Cohomology: An Algebraic Introduction with Geometric Applications . Cambridge : Cambridge University Press .
  • Brodmann , M. , Sharp , R. Y. ( 2002 ). On the dimension and multiplicity of local cohomology modules . Nagoya Math. J. 167 : 217 – 233 .
  • Cuong , N. T. , Nhan , L. T. ( 2002 ). On the Noetherian dimension of Artinian modules . Vietnam J. Math. 30 : 121 – 130 .
  • Cuong , N. T. , Dung , N. T. , Nhan , L. T. ( 2007 ). Top local cohomology and the catenaricity of the unmixed support of a finitely generated module . Comm. Algebra 35 : 1691 – 1701 .
  • Ferrand , D. , Raynaud , M. ( 1970 ). Fibres formelles d'un anneau local Noetherian . Ann. Sci. Ecole Norm. Sup. 3 : 295 – 311 .
  • Kirby , D. ( 1990 ). Dimension and length of Artinian modules . Quart. J. Math. Oxford. 41 : 419 – 429 .
  • Macdonald , I. G. ( 1973 ). Secondary representation of modules over a commutative ring . Symposia Mathematica 11 : 23 – 43 .
  • Matsumura , H. ( 1986 ). Commutative Ring Theory . Cambridge : Cambridge University Press .
  • McAdam , S. , Ratliff , L. J. ( 1977 ). Semi-local taut rings . Indiana Univ. Math. J. 26 : 73 – 79 .
  • Nagata , M. ( 1962 ). Local Rings . New York : Interscience .
  • Nhan , L. T. , An , T. N. ( 2009 ). On the unmixedness and the universal catenaricity of local rings and local cohomology modules . J. Algebra 321 : 303 – 311 .
  • Roberts , R. N. ( 1975 ). Krull dimension for Artinian modules over quasi local commutative rings . Quart. J. Math. Oxford 26 : 269 – 273 .
  • Sharp , R. Y. ( 1975 ). Some results on the vanishing of local cohomology modules . Proc. London Math. Soc. 30 : 177 – 195 .
  • Sharp , R. Y. ( 1975 ). Secondary representations for injective modules over commutative Noetherian rings . Proc. Edinburgh Math. Soc. 20 : 143 – 151 .
  • Tang , Z. , Zakeri , H. ( 1994 ). Co-Cohen-Macaulay modules and modules of generalized fractions . Comm. Algebra. 22 : 2173 – 2204 .
  • 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:

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.