# ON THE INTEGRAL CLOSURES OF IDEALS

Ansari-Toroghy, H.;Dorostkar, F.

• Accepted : 2007.11.18
• Published : 2007.12.25
• 28 1

#### 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.)

#### Keywords

reduction;integral dependence;integral closure;associated primes

#### References

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#### Cited by

1. TIGHT CLOSURE OF IDEALS RELATIVE TO MODULES vol.32, pp.4, 2010, https://doi.org/10.5831/HMJ.2010.32.4.675
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