Practice problem
Let ϕ :A→B\phi\colon A\to Bϕ:A→B be a ring homomorphism. If ℘\wp℘ is a prime ideal of AAA, describe Spec(B℘)\operatorname{Spec}(B_\wp)Spec(B℘), the set of prime ideals of B℘:=(A−℘)−1B=B⊗AA℘.B_\wp := (A-\wp)^{-1}B= B\otimes_A A_\wp.B℘:=(A−℘)−1B=B⊗AA℘.
Primes of B℘B_\wpB℘ correspond to primes of BBB containing ℘B\wp B℘B.
Primes of B℘B_\wpB℘ correspond to primes of BBB contained in ℘B\wp B℘B.
Primes of B℘B_\wpB℘ correspond to primes of BBB disjoint from ϕ(A∖℘)\phi(A\setminus \wp)ϕ(A∖℘).
Primes of B℘B_\wpB℘ correspond to primes of BBB pulling back to ℘\wp℘ under ϕ\phiϕ.
Type a concept, like “slope” or “photosynthesis”.