호남수학학술지 (Honam Mathematical Journal)

  • 제24권1호
  • /
  • Pages.1-8
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  • 2002
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

ASYMPTOTIC STABILITY OF SOME SEQUENCES RELATED TO INTEGRAL CLOSURE

  • ANSARI-TOROGHY, H. (Dept. of Mathematics, Faculty of Science, University of Guilan)
  • 투고 : 2001.10.02
  • 발행 : 2002.07.30
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초록

In this paper we will show that if E is an injective module over a commutative ring A, then the sequence of sets $Ass_{A}(A/I^{n})^{*(E)}),\;n{\in}N,$ is increasing and ultimately constant. Also we will obtain some results concerning the integral closure of ideals related to some modules.

키워드

참고문헌

  1. Communication in Algebra v.26 no.2 Associated and Coassociated primes Ansari-Toroghy, H.
  2. v.23 Injective prime avoidance property and related results Ansari-Toroghy, H.
  3. Quart. J. Math. Oxford v.42 no.2 Integral closures of ideals relative to injective modules over commutative Noetherian rings Ansari-Toroghy, H.;Sharp, R.Y.
  4. Pacific J. Math. v.8 Injective modules over Noerherian rings Matlis, E.
  5. Commutative Algebra Matsumura, H.
  6. Comm. Algebra v.20 no.2 Asymptotic attached prime ideals related to injective modules Melkerson, L.;Schenzel, P.
  7. Proc. Cambridge Philos. Soc. v.50 Reductions of ideals in local rings Northcott, D.G.;Rees, D.
  8. Pacific J. Math. v.111 On asymptotic prime divisors Ratliff, L.J. Jr.
  9. A method for study of Artinian modules, with an application to asymptotic behaviour;Commutative Algebra, Math Sience Research Inst. Publ. No. 15 Sharp, R.Y.
  10. Steps in Commutative Algebra Sharp, R.Y.
  11. J. London Soc. v.37 no.2 Reductions and integral closures of ideals relative to an Artinian module Sharp, R.Y.;Taherizadeh, A.J.
  12. Comm. Algebra v.23 Coassociated primes Yassemi, S.