ASYMPTOTIC STABILITY OF SOME SEQUENCES RELATED TO INTEGRAL CLOSURE

  • ANSARI-TOROGHY, H. (Dept. of Mathematics, Faculty of Science, University of Guilan)
  • Received : 2001.10.02
  • Published : 2002.07.30

Abstract

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.

Keywords

integral closure;associated primes;asymptotic stability

References

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