SOME CHARACTERIZATIONS OF COHEN-MACAULAY MODULES IN DIMENSION > s

Title & Authors
SOME CHARACTERIZATIONS OF COHEN-MACAULAY MODULES IN DIMENSION > s
Dung, Nguyen Thi;

Abstract
Let (R,m) be a Noetherian local ring and M a finitely generated R-module. For an integer s > -1, we say that M is Cohen-Macaulay in dimension > s if every system of parameters of M is an M-sequence in dimension > s introduced by Brodmann-Nhan [1]. In this paper, we give some characterizations for Cohen-Macaulay modules in dimension > s in terms of the Noetherian dimension of the local cohomology modules $\small{H^i_m(M)}$, the polynomial type of M introduced by Cuong [5] and the multiplicity e($\small{\underline{x}}$;M) of M with respect to a system of parameters $\small{\underline{x}}$.
Keywords
Cohen-Macaulay modules in dimension > s;M-sequence in dimension > s;multiplicity;Noetherian dimension;local cohomology modules;
Language
English
Cited by
References
1.
M. Brodmann and L. T. Nhan, A finiteness result for associated primes of certain Ext-modules, Comm. Algebra 36 (2008), no. 4, 1527-1536.

2.
M. Brodmann and R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge University Press, 1998.

3.
W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, 1993.

4.
N. T. Cuong, On the dimension of the non-Cohen-Macaulay locus of local rings admitting dualizing Complexes, Math. Proc. Cambridge. Philos. Soc. 109 (1991), no. 3, 479-488.

5.
N. T. Cuong, On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain system of parameters in local rings, Nagoya Math. J. 125 (1992), 105-114.

6.
N. T. Cuong, M. Morales, and L. T. Nhan, On the length of generalized fractions, J. Algebra 265 (2003), no. 1, 100-113.

7.
N. T. Cuong and L. T. Nhan, On Noetherian dimension of Artinian modules, Vietnam J. Math. 30 (2002), no. 2, 121-130.

8.
N. T. Cuong, L. T. Nhan, and N. T. K. Nga, On pseudo supports and non-Cohen-Macaulay locus of finitely generated modules, J. Algebra 323 (2010), no. 10, 3029-3038.

9.
N. T. Cuong, P. Schenzel, and N. V. Trung, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57-73.

10.
D. Ferrand and M. Raynaud, Fibres formelles d'un anneau local Noetherian, Ann. Sci. Ec. Norm. Sup. (4) 3 (1970), 295-311.

11.
M. Hellus, On the set of associated primes of a local cohomology modules, J. Algebra 237 (2001), no. 1, 406-419.

12.
T. Kawasaki, On arithmetic Macaulayfication of Noetherian rings, Trans. Amer. Math. Soc. 354 (2002), no. 1, 123-149.

13.
D. Kirby, Dimension and length for Artinian modules, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 164, 419-429.

14.
R. Lu and Z. Tang, The f-depth of an ideal on a module, Proc. Amer. Math. Soc. 130 (2002), no. 7, 1905-1912.

15.
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.

16.
H. Matsumura, Commutative Ring Theory, Cambridge, Cambridge University Press, 1986.

17.
L. T. Nhan, On generalized regular sequences and the finiteness for associated primes of local cohomology modules, Comm. Algebra 33 (2005), no. 3, 793-806.

18.
L. T. Nhan and M. Morales, Generalized f-modules and the associated prime of local cohomology modules, Comm. Algebra 34 (2006), no. 3, 863-878.

19.
R. N. Roberts, Krull dimension for Artinian modules over quasi-local commutative rings, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 103, 269-273.

20.
N. V. Trung, Toward a theory of generalized Cohen-Macaulay modules, Nagoya Math J. 102 (1986), 1-49.

21.
N. Zamani, Cohen-Macaulay modules in dimension > s and results on local cohomology, Comm. Algebra 37 (2009), no. 4, 1297-1307.