Lifting chains of prime ideals
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.