Lifting chains of prime ideals
Brenner, Holger
Original · EN
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.
English translation
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