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Paper   IPM / M / 8387
School of Mathematics
  Title:   Filter rings under flat base change
  Author(s):  P. Sahandi (and S. Yassemi)
  Status:   Published
  Journal: Algebra Colloq.
  No.:  3
  Vol.:  15
  Year:  2008
  Pages:   463-470
  Supported by:  IPM
  Abstract:
Let φ: (R,\fm)→ (S,\fn) be a flat local homomorphism of rings. It is proved that

    (a) If dimS/\fmS > 0, then S is a filter ring if and only if R and k(\fp)⊗R\fp S\fq are Cohen-Macaulay for all \fq ∈ \Spec(S)\{\fn} and \fp = \fq∩R, and S/\fpS is catenary and equidimensional for all minimal prime ideal \fp of R.
    (b) If dimS/\fmS=0, then S is a filter ring if and only if R is a filter ring and k(\fp)⊗R\fp S\fq is Cohen-Macaulay for all \fq ∈ \Spec (S)\{\fn} and \fp = \fq∩R, and S/\fpS is catenary and equidimensional for all minimal prime ideal \fp of R.
As an application, it is shown that for a k-algebra R and an algebraic field extension K of k, if KkR is locally equidimensional then R is locally filter ring if and only if KkR is locally filter ring.


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