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arXiv · math/0209296

Lifting chains of prime ideals

Holger Brenner
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Abstract

We give an elementary proof that for a ring homomorphism A -> B, satisfying the property that every ideal in A is contracted from B, the following property holds: for every chain of prime ideals p_0 \subset ... \subset p_r in A there exists a chain of prime ideals q_0 \subset ... \subset q_r in B such that q_i \cap A = p_i.

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Holger Brenner. 2002-09-23. Lifting chains of prime ideals. https://arxiv.org/abs/math/0209296

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