WEAKLY LASKERIAN, WEAKLY COFINITE MODULES AND GENERALIZED LOCAL COHOMOLOGY
WEAKLY LASKERIAN, WEAKLY COFINITE MODULES AND GENERALIZED LOCAL COHOMOLOGY
Let R be a commutative Noetheran ring, I an ideal of R and M be a finitely generated projective R-module. Let N be an R module and t a non-negative integer such that Extt R(M/IM, N) is weakly Laskerian. Then for any weakly Laskerian submodule U of the first non I-weakly cofinite module HtI(M, N), the R-module HomR(M/IM, HtI(M, N)/U) is weakly Laskerian. As a consequence the set of associated primes of HtI(M, N)/U is finite.
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- M. Brodmann and F. Lashgari, A finiteness result for associated primes of local cohomology, Proc. Amer. Math. Soc., 128 (2000), 2851-2853.
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1993.
- M. Brodmann and R. Y. Sharp, Local Cohomology: An algebraic introduction with geometric applications, Cambridge University Press, Cambridge, 1998.
- L. W. Christensen, Gorenstein Dimension, Lecture Notes in Math., 174 (2000).
- N. T. Cuong and N. V. Hoang, Some finiteness properties of generalized local cohomology modules, East-West J. Math., 7 (2005), 107-115.
- N. T. Cuong and N. V. Hoang, On the vanishing and the finiteness of supports of generalized local cohomology modules, arXiv:0705.4553v1, (2007).
- K. Divaani-Aazar and A. Mafi, Associated primes of local cohomology modules, Proc. Amer. Math. Soc., 133 (2004), 655-660.
- K. Divaani-Aazar and A. Mafi, Associated primes of local cohomology modules of weakly Laskerian modules, Comm. Algebra, 34 (2006), 681-690.
- K. Divaani-Aazar and M. A. Esmkhani, Artinianess of local cohomology mod- ules of ZD-modules, Comm. Algebra, 33 (2005), 2857-2863.
- J. Herzog, Komplexe, Aufl¨osungen und Dualitat in der lokalen algebra, Habil- itationsschrift, Universit¨at regensburg, 1970.
- J. Herzog and N. Zamani, Duality and vanishing of generalized local cohomo- logy, Arch. Math. (Basel), 81 (2003) 512-519.
- C. Huneke, Problems on local cohomology, Free resolutions in commutative algebra and algebraic geometry, Res. Nots Math., 2 (1992), 93-108.
- M. Katzman, An example of an infinite set of associated primes of a local cohomology modules, J. Algebra, 252 (2002), 161-166.
- G. Lyubeznik, A partial survay of local cohomology, local cohomology and its applications. Lecture notes in Pure and Appl. Math., 228 (2002), 121-154.
- J. Rotman, An Introduction to Homological Algebra, Academic Press, San Diago, 1979.
- A. K. Singh, p-torsion elements in local cohomology modules, Math. Res. Lett., 7 (2000), 165-176.
- B. Snapp, Generalized local cohomology and the canonical element conjecture, J. Pure Appl. Algebra, doi:10.1016/j.jpaa. (2007) 07.017.
- S. Yassemi and M. T. Dibaei, Associated primes and cofiniteness of local co- homology modules, Manuscripta Math., 117 (2005), 199-205.
- H. Z¨oschinger, Minimax modules, J. Algebra, 102 (1986), 1-32. Naser Zamani Faculty of Science
- University of Mohaghegh Ardabili Ardabil, Iran
- e-mail: naserzaka@yahoo.com
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI