SOME RESULTS ON COFINITE MODULES

Let R be a Noetherian ring and a be a proper ideal of R. We generalize the Rees characterization of grade for a-cofinite modules and as a consequence, we extend Grothendieck’s Non-vanishing Theorem. We also generalize the classical Auslander-Buchsbaum and Bass formulas.

Keywords:

Auslander-Buchsbaum formula, Bass formula, local cohomology cofinite module,

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M. Aghapournahr and L. Melkersson, CoŞniteness and coassociated primes of local cohomology modules, Math. Scand., 105(7) (2009), 161-170.
K. Bahmanpour and R. Naghipour, CoŞniteness of local cohomology modules for ideals of small dimension, J. Algebra, 321 (2009), 1997-2011.
R. G. Belshoﬀ, E. E. Enochs and J. R. Garcia Rozas, Generalized Matlis du- ality, Proc. Amer. Math. Soc., 128(5) (2000), 1307-1312.
M. P. Brodmann and R. Y. Sharp, Local Cohomology: An algebraic intro- duction with geometric applications, Cambridge University Press, Cambridge, W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge 1993.
S. Choi and S. Iyengar, On the depth formula for modules over local rings, Comm. Algebra, 29(7) (2001), 3135-3143.
L. G. Chouinard II, On Şnite weak and injective dimension, Proc. Amer. Math. Soc., 60 (1976), 57-60.
D. DelŞno and T. Marley, CoŞnite modules and local cohomology, J. Pure Appl. Algebra, 121(1) (1997), 45-52.
A. Grothendieck, Cohomologie locale des faisceaux coh´erents et th´eor`emes de Lefshetz locaux et globaux (SGA2). North-Holland, Amsterdam, 1968.
R. Hartshorne, Aﬃne duality and coŞniteness, Invent. Math., 9 (1970), 145
M. Hellus, On the set of associated primes of a local cohomology module, J. Algebra, 237(1) (2001), 406-419.
C. Huneke, Problems on Local Cohomology, Free resolutions in commutative algebra and algebraic geometry. Res. Notes Math., 2 (1992), 93-108.
C. Huneke and J. Koh, CoŞniteness and vanishing of local cohomology modules, Math. Proc. Camb. Phil. Soc., 110 (1991), 421-429.
C. Huneke and R. Y. Sharp, Bass numbers of local cohomology modules, Trans. Amer. Math. Soc., 339(2) (1993), 765-779.
F. Ischebeck, Eine Dualit¨at zwischen den Funktoren Ext und Tor, J. Algebra, (1969), 510-531.
M. Katzman, An example of an inŞnite set of associated primes of a local cohomology module, J. Algebra, 252(1) (2002), 161-166.
K.-I. Kawasaki, CoŞniteness of local cohomology modules for principal ideals, Bull. London. Math. Soc., 30(3) (1998),241-246.
G. Lyubeznik, Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: the unramiŞed case, Comm. Algebra, 28(12) (2000), 5867-5882.
A. MaŞ, Some results on local cohomology modules, Arch. Math. (Basel), 87(3) (2006), 211-216.
L. Melkersson, Properties of coŞnite modules and applications to local coho- mology, Math. Proc. Camb. Phil. Soc., 125(3) (1999), 417-423.
L. Melkersson, Modules coŞnite with respect to an ideal, J. Algebra, 285(2) (2005), 649-668.
M. S. Osborne, Basic Homological Algebra, Springer-Verlag, New York, 2000.
J. Rotman, An Introduction to Homological Algebra, Academic Press, San Diego, 1979.
P. Rudlof, On minimax and related modules, Canad. J. Math., 44(1) (1992), 166.
A. K. Singh, p-torsion elements in local cohomology modules, Math. Res. Lett., (2000), 165-176.
S. Yassemi, Width of complexes of modules, Acta. Math. Vietnam, 23 (1998), 169.
K.-I. Yoshida, CoŞniteness of local cohomology modules for ideals of dimension one, Nagoya Math. J., 147 (1997), 179-191.
H. Z¨oschinger, Minimax modules, J. Algebra, 102(1) (1986), 1-32.
H. Z¨oschinger,Uber die Maximalbedingung f¨ur radikalvolle Untermoduln, ¨ Hokkaido Math. J., 17(1) (1988), 101-116. A. R. Naghipour
Department of Mathematics Faculty of Science Shahrekord University Shahrekord, Iran e-mail: naghipour@sci.sku.ac.ir

International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

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