Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE INTEGRAL CLOSURES OF IDEALS

  • Ansari-Toroghy, H. (Department of Mathematics, Faculty of Science, University of Guilan) ;
  • Dorostkar, F. (Department of Mathematics, Faculty of Science, University of Guilan)
  • Received : 2007.04.11
  • Accepted : 2007.11.18
  • Published : 2007.12.25
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Abstract

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

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References

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  2. 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