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TIGHT CLOSURE OF IDEALS RELATIVE TO MODULES

  • Ansari-Toroghy, H. (Department of Mathematics Faculty of Science University of Guilan) ;
  • Dorostkar, F. (Department of Mathematics Faculty of Science University of Guilan)
  • Received : 2010.02.22
  • Accepted : 2010.06.16
  • Published : 2010.12.25

Abstract

In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.

Keywords

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. https://doi.org/10.1093/qmath/42.1.393
  2. H. Ansari-Toroghy, Secondary representation of some modules over a commutative ring, Acta Math. Hungar., (3) 100 (2003), 257-262. https://doi.org/10.1023/A:1025097610892
  3. H. Ansari-Toroghy and F. Dorostkar, On the integral closure of ideals, Honam Math. J., (4) 29 (2007), 653-666. https://doi.org/10.5831/HMJ.2007.29.4.653
  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. https://doi.org/10.1090/S0002-9939-1964-0162814-3
  10. I. Swanson and C. Huneke, Integral closure of ideals, rings, and modules, Cambridge Univ. Press, New York, 2006.

Cited by

  1. THE TIGHT INTEGRAL CLOSURE OF A SET OF IDEALS RELATIVE TO MODULES vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.231