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Paper   IPM / M / 467
School of Mathematics
  Title:   Quintessential primes and ideal topologies over a module
  Author(s):  R. Naghipour
  Status:   Published
  Journal: Comm. Algebra
  No.:  8
  Vol.:  29
  Year:  2001
  Pages:   3495-3506
  Supported by:  IPM
Let I be an ideal of a Noetherian ring R, N a finitely generated R-module and let S be a multiplicatively closed subset of R. We define the n-the (S)-symbolic power of I w.r.t. N as S(InN)=∪sS(In N:N s). The purpose of this paper is to show that the topologies defined by {In N}n ≥ 0 are equivalent (resp. linearly equivalent) if and only if S is disjoint from the quintessential (resp. essential) primes of I w.r.t. N.

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