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/℘B)\operatorname{Spec}(B/\wp B)Spec(B/℘B), the set of prime ideals of B/℘B=B⊗AA/℘.B/\wp B = B\otimes_A A/\wp.B/℘B=B⊗AA/℘.
Primes of B/℘BB/\wp BB/℘B correspond to primes of BBB containing ℘B\wp B℘B.
Primes of B/℘BB/\wp BB/℘B correspond to primes of BBB contained in ℘B\wp B℘B.
Primes of B/℘BB/\wp BB/℘B correspond to primes of BBB disjoint from ϕ(A∖℘)\phi(A\setminus \wp)ϕ(A∖℘).
Primes of B/℘BB/\wp BB/℘B correspond to primes of BBB pulling back to ℘\wp℘ under ϕ\phiϕ.
Type a concept, like “slope” or “photosynthesis”.