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| Paper IPM / M / 8387 |
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| Abstract: | |
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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. Download TeX format |
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