Lifting chains of prime ideals
classification
🧮 math.AC
keywords
subsetidealsprimechaineverypropertychainscontracted
read the original 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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