# SOME PROPERTIES OF GENERALIZED LOCAL HOMOLOGY AND COHOMOLOGY MODULES

• Nam, Tran Tuan ;
• Minh, Nguyen Duc
• Received : 2012.09.10
• Published : 2013.11.30
• 65 3

#### Abstract

We study some properties of representable generalized local homology modules. By duality, we get some properties of good generalized local cohomology modules.

#### Keywords

Artinian module;finitely generated module;representable module;local homology;local cohomology

#### References

1. H. Ansari-Toroghy, Secondary representation of some modules over a commutative ring, Acta Math. Hungar. 100 (2003), no. 3, 257-262. https://doi.org/10.1023/A:1025097610892
2. M. P. Brodmann and R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge University Press 1998.
3. N. T. Cuong and T. T. Nam, The I-adic completion and local homology for Artinian modules, Math. Proc. Cambridge Philos. Soc. 131 (2001), no. 1, 61-72.
4. N. T. Cuong and T. T. Nam, A local homology theory for linearly compact modules, J. Algebra 319 (2008), no. 11, 4712-4737. https://doi.org/10.1016/j.jalgebra.2007.11.030
5. J. Herzog, Komplexe, Auflosungen und dualitat in der localen Algebra, Habilitation-schrift Univ. Regensburg, 1970.
6. K. Khashyarmanesh, M. Yassi, and A. Abbasi, A new version of local-global principle for annihilations of local cohomology modules, Colloq. Math. 100 (2004), no. 2, 213-219. https://doi.org/10.4064/cm100-2-5
7. I. G. Macdonald, Secondary representation of modules over a commutative ring, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971), pp. 23-43. Academic Press, London, 1973.
8. T. T. Nam, Generalized local homology for artinian modules, Algebra Colloquium (to appear).
9. T. T. Nam, Generalized local homology, Proceedings of the 4th Japan-Vietnam Joint Seminar, Meiji University, Japan (2009), 217-235.
10. T. T. Nam, A finiteness result for co-associated and associated primes of generalized local homology and cohomology modules, Comm. Algebra 37 (2009), no. 5, 1748-1757. https://doi.org/10.1080/00927870802216396
11. T. T. Nam, On the non-vanishing and the artinianness of generalized local cohomology modules, Journal of Algebra and Its Applications (to appear).
12. S. Rezaei, Some results on local homology and local cohomology modules, Illinois Journal of Mathematics (to appear).
13. S. Yassemi, Coassociated primes, Comm. Algebra 23 (1995), no. 4, 1473-1498. https://doi.org/10.1080/00927879508825288