Nihonkai Mathematical Journal

On the Category of Confinite Modules for Principal Ideals

Ken-Ichiroh Kawasaki

Abstract

In this paper, it is pointed out that ${\mathcal M}(A, I)_{cof}$ is an Abelian full subcategory of the category ${\mathcal M}(A)$ consisting of all $A$-modules for a principal ideal $I$ over a noetherian ring $A$.

Article information

Source
Nihonkai Math. J., Volume 22, Number 2 (2011), 67-71.

Dates
First available in Project Euclid: 14 June 2012

https://projecteuclid.org/euclid.nihmj/1339696712

Mathematical Reviews number (MathSciNet)
MR2952818

Zentralblatt MATH identifier
1247.14003

Citation

Kawasaki, Ken-Ichiroh. On the Category of Confinite Modules for Principal Ideals. Nihonkai Math. J. 22 (2011), no. 2, 67--71. https://projecteuclid.org/euclid.nihmj/1339696712

References

• K. Eto and K. -i. Kawasaki, A characterization of cofinite complexes over complete Gorenstein domains, J. Commut. Algebra, 3 No. 4, Winter, (2011), 537–550.
• D. Delfino and T. Marley, Cofinite modules and local cohomology, J. Pure Appl. Algebra, 121, (1997), 45–52.
• R. Hartshorne, Affine duality and cofiniteness, Invent. Math., 9, (1970), 145–164.
• C. Huneke and J. Koh, Cofiniteness and vanishing of local cohomology modules, Math. Proc. Cambridge Philos. Soc., 110 No. 3, (1991), 421–429.
• K. -i. Kawasaki, Cofiniteness of local cohomology modules for principal ideals, Bull. Lond. Math. Soc., 30, (1998), 241–246.
• K. -i. Kawasaki, On a category of cofinite modules which is Abelian, Math. Z., 269 Issue 1, (2011), 587-608.
• J. Rotman, An introduction to homological algebra, Pure and applied mathematics, vol. 226, Academic press, Inc., Harcourt Brace $\and$ Company, Publishers, Boston, San Diego, New York, London, Sydney, Tokyo, Toronto, (1979).