JOURNAL BROWSE
Search
Advanced SearchSearch Tips
TIGHT CLOSURE OF IDEALS RELATIVE TO MODULES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 4,  2010, pp.675-687
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.4.675
 Title & Authors
TIGHT CLOSURE OF IDEALS RELATIVE TO MODULES
Ansari-Toroghy, H.; Dorostkar, F.;
  PDF(new window)
 Abstract
In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.
 Keywords
F-reduction;Tight closure;Tight dependent;Associated prime ideal;
 Language
English
 Cited by
1.
THE TIGHT INTEGRAL CLOSURE OF A SET OF IDEALS RELATIVE TO MODULES, Honam Mathematical Journal, 2016, 38, 2, 231  crossref(new windwow)
 References
1.
H. Ansari-Toroghy and R.Y. Sharp, Integral closure of ldeals relative to injective modules over commutative Noetherian rings, Quart. J. Math. Oxford, (2) 42 (1991), 393-402. crossref(new window)

2.
H. Ansari-Toroghy, Secondary representation of some modules over a commutative ring, Acta Math. Hungar., (3) 100 (2003), 257-262. crossref(new window)

3.
H. Ansari-Toroghy and F. Dorostkar, On the integral closure of ideals, Honam Math. J., (4) 29 (2007), 653-666. crossref(new window)

4.
M. Brodmann, Asymptotic stability of $Ass(M/I^{b}M)$, Proc. Amer. Meth. Soc., 74 (1979), 16-18.

5.
M. Hochster and C. Huneke, Tight closure, invariant theory, and Briancon-Skoda theorem, J. Amer. Math. Soc., (1) 3 (1990), 31-116.

6.
I. G. Macdonald, Secondary representation of modules over a commutative ring, Symp. Math. XI(1973), 23-43.

7.
H. Matsumura, Commutative Algebra, Benjamin, New York, 1970.

8.
S. McAdam, Asymptotic prime divisors, Lecture Notes in Mathematics 1023, Springer, Berlin, 1983.

9.
J. W. Petro, Some results on the asymptotic completion of an ideal, Proc. Amer. Math. Soc., 15 (1964), 519-524. crossref(new window)

10.
I. Swanson and C. Huneke, Integral closure of ideals, rings, and modules, Cambridge Univ. Press, New York, 2006.