Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T05:44:16.912Z Has data issue: false hasContentIssue false
  • English
  • Français

Co-Cohen-Macaulay Artinian modules over commutative rings

Published online by Cambridge University Press:  18 May 2009

I. H. Denizler  and
R. Y. Sharp
I. H. Denizler
Affiliation:
Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH
R. Y. Sharp
Affiliation:
Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [7], Z. Tang and H. Zakeri introduced the concept of co-Cohen-Macaulay Artinian module over a quasi-local commutative ring R (with identity): a non-zero Artinian R-module A is said to be a co-Cohen-Macaulay module if and only if codepth A = dim A, where codepth A is the length of a maximalA-cosequence and dimA is the Krull dimension of A as defined by R. N. Roberts in [2]. Tang and Zakeriobtained several properties of co-Cohen-Macaulay Artinian R-modules, including a characterization of such modules by means of the modules of generalized fractions introduced by Zakeri and the present second author in [6]; this characterization is explained as follows.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 3 , September 1996 , pp. 359 - 366
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.O'Carroll, L., On the generalized fractions of Sharp and Zakeri, J. London Math. Soc. (2) 28 (1983), 417–427.CrossRefGoogle Scholar
2.Roberts, R. N., Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math. Oxford Ser.(2) 26 (1975), 269–273.CrossRefGoogle Scholar
3.Sharp, R. Y., A method for the study of Artinian modules, with an application to asymptotic behavior, Commutative algebra. Proceedings of the microprogram held in Berkeley, California, 15 June—2 July 1987, Mathematical Sciences Research Institute Publications 15 (Springer, 1989), 443–465.CrossRefGoogle Scholar
4. Sharp, R. Y., Artinian modules over commutative rings, Math. Proc. Cambridge Philos. Soc. III (1992), 25–33.CrossRefGoogle Scholar
5.Sharp, R. Y. and Tiras, Y., Asymptotic behaviour of integral closures of ideals relative to Artinian modules, J. Algebra 153 (1992), 262–269.CrossRefGoogle Scholar
6.Sharp, R. Y. and Zakeri, H., Modules of generalized fractions, Mathematika 29 (1982), 32–41.CrossRefGoogle Scholar
7.Tang, Z. and Zakeri, H., Co-Cohen-Macaulay modules and modules of generalized fractions, Comm. Algebra 22 (1994), 2173–2204.CrossRefGoogle Scholar