Lifting chains of prime ideals

2002/09/23 by Holger Brenner
Mathematics · #math.AC #msc:13B24

paper · pdf

published as J. Pure Appl. Algebra 179 (2003), 1 - 5. · to appear in Journal of pure and applied algebra

arxiv created 2002/09/23 · arxiv updated 2009/11/30

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 p₀ ⊂ ... ⊂ p_r in A there exists a chain of prime ideals q₀ ⊂ ... ⊂ q_r in B such that q_i ∩ A = p_i.

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