COHEN-MACAULAY MODULES OVER NOETHERIAN LOCAL RINGS

Title & Authors
COHEN-MACAULAY MODULES OVER NOETHERIAN LOCAL RINGS
Bahmanpour, Kamal;

Abstract
Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth($\small{M/I^nM}$)
Keywords
balanced big Cohen-Macaulay modules;Cohen-Macaulay modules;local cohomology modules;quasi regular sequences;
Language
English
Cited by
1.
On almost Cohen–Macaulayness of quotient modules, Rendiconti del Circolo Matematico di Palermo (1952 -), 2017
References
1.
M. Brodmann, Asymptotic stability of Ass(M/InM), Proc. Amer.Math. Soc. 74 (1979), no. 1, 16-18.

2.
M. Brodmann, The asymptotic nature of the analytic spread, Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 1, 35-39.

3.
M. P. Brodmann and R. Y. Sharp, Local Cohomology: an algebraic introduction with geometic applications, Cambridge University Press, Cambridge, 1998.

4.
A. Cherrabi, Quasi-regular sequences and regular sequences, Comm. Algebra 39 (2011), no. 1, 184-188.

5.
D. Ferrand and M. Rayanaud, Fibres formelles d'un anneau local Noetherien, Ann. Sci. Ecole Norm. Sup. 3 (1970), 295-311.

6.
M. Hochster, Cohen-Macaulay modules, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), pp. 120-152. Lecture Notes in Math., Vol. 311, Springer, Berlin, 1973.

7.
M. Hochster, Topics in the homological theory of modules over commutative rings, C.B.M.S. Regional Conference Series in Mathematics No. 24, Providence, R.I.: AMS, 1975.

8.
M. Hochster, Big Cohen-Macaulay modules and algebras and embeddability in rings of Witt vectors, Conference on Commutative Algebra975 (Queen's Univ., Kingston, Ont., 1975), pp. 106-195. Queen's Papers on Pure and Applied Math., No. 42, Queen's Univ., Kingston, Ont., 1975.

9.
H. Matsumura, Commutative Ring Theory, Cambridge Univ. Press, Cambridge, UK, 1986.

10.
L. Melkersson, On asymptotic stability for sets of prime ideals connected with the powers of an ideal, Math. Proc. Cambridge Philos. Soc. 107 (1990), no. 2, 267-271.

11.
L. J. Ratliff, Jr., On the prime divisors of \$I^n\$, n large, Michigan Math. J. 23 (1976), 337-352.

12.
H. Zoschinger, Minimax modules, J. Algebra 102 (1986), no. 1, 1-32.