호남수학학술지 (Honam Mathematical Journal)

  • 제29권4호
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  • Pages.653-666
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  • 2007
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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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)
  • 투고 : 2007.04.11
  • 심사 : 2007.11.18
  • 발행 : 2007.12.25
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초록

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.)

키워드

참고문헌

  1. H. Ansari-Toroghy and R.Y. Sharp, Integral closure of ideals relative to injective modules over commutative Noetherian rings, Quart. J. Math., (2) 42 (1991), 393-402. https://doi.org/10.1093/qmath/42.1.393
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  10. R.Y. Sharp and A.J. Taherizadeh, Reductions and integral closures of ideals relative to an Artinian module, J. London Math. Soc., (2) 37 (1988), 203-218. https://doi.org/10.1112/jlms/s2-37.2.203
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피인용 문헌

  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