Lifting chains of prime ideals
Holger Brenner
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 ⊂ ... ⊂ pr in A there exists a chain of prime ideals q0 ⊂ ... ⊂ qr in B such that qi A = pi.
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