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△-CLOSURES OF IDEALS WITH RESPECT TO MODULES
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  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 1,  2008, pp.101-113
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.1.101
 Title & Authors
△-CLOSURES OF IDEALS WITH RESPECT TO MODULES
Ansari-Toroghy, H.; Dorostkar, F.;
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 Abstract
Let M be an arbitrary module over a commutative Noetherian ring R and let be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of -closure and -dependence of an ideal with respect to M and obtain some related results.
 Keywords
-reduction;-dependence;-closure;associated primes;attached primes;and asymptotic behavior;
 Language
English
 Cited by
 References
1.
H. Ansari-Toroghy and R.Y. Sharp, Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings, Proc. Edinburgh Math. Soc. (2) 34 (1991), 155-160. crossref(new window)

2.
H. Ansari-Toroghy and R.Y. Sharp, Integral closure of ideals relative to injective modules over commutative Noetherian rings, Quart. J. Math. Oxford, (2) 42 (1991), 393-402. crossref(new window)

3.
L. Melkersson, P. Schenzel, Asymptotic attached prime ideals related to injective modules, Comm. Algebra (2) 20 (1992), 583-590. crossref(new window)

4.
R. Naghipour and M. Sedghi, ${\Delta}-Reductions$ and ${\Delta}-closures$ of ideals with respect to an Artinian module, Communications in Algebra, 34 (2006), 763-777. crossref(new window)

5.
L.J. Ratliff, Jr., ${\Delta}-closures$ of ideals and rings, Trans. Amer. Math. Soc., 313 (1989), 221-247.

6.
L.J. Ratliff, Jr. and D. E. Rush, ${\Delta}-Reductions$ of modules, Communications in Algebra, (8) 21 (1993), 2667-2685. crossref(new window)

7.
D. Rees and R.Y. Sharp, On a theorem of B. Teissier on multiplicities of ideals in local rings, J. London Math. Soc. (2)18 (1978), 449-463. crossref(new window)