Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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TIGHT CLOSURE OF IDEALS RELATIVE TO SOME MODULES

  • Dorostkar, F. (Department of Pure Mathematics, University of Guilan) ;
  • Khosravi, R. (Department of Pure Mathematics, University of Guilan)
  • Received : 2016.11.08
  • Accepted : 2017.10.09
  • Published : 2017.12.25
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Abstract

In this paper we consider the tight closure of an ideal relative to a module whose its zero submodule has a primary decomposition.

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References

  1. H. Ansari-Toroghy and F. Dorostkar, Tight closure of ideals relative to modules, Honam Math. J., 32(4) (2010), 675-687. https://doi.org/10.5831/HMJ.2010.32.4.675
  2. N. Bourbaki, Algebra commutative, Hermann, Paris, 1972.
  3. F. Dorostkar and R. Khosravi, F-Regularity Relative To Modules, Journal of Algebra and Related Topics, 3(1) (2015), 41-50.
  4. D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate texts in mathematics 150, Springer-Verlage, 1995.
  5. M. Hochster and C. Huneke, Tight closure, invariant theory, and Briancon-Skoda theorem, J. of the Amer. Math. Soc., 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, 2nd edition, Mass., 1980.
  8. H. Matsumura, Commutative ring theory, Cambridge Univ. press, 1986.
  9. I. Nishitani, Associated prime ideals of the dual of an artinian module relative to an injective module, Comm. in Algebra, 22(7) (1994), 2651-2667. https://doi.org/10.1080/00927879408824984
  10. I. Swanson and C. Huneke, Integral closure of ideals, rings, and modules, Cambridge Univ. Press, New York, 2006.
  11. S. Yassemi, Coassociated primes of modules over a commutative ring, Math Scand. , 80 (1997), 175-187. https://doi.org/10.7146/math.scand.a-12617