Practice problem
Let AAA be a ring and ℘\wp℘ a prime ideal of AAA. When does ℘=ker(A→A℘/℘A℘)\wp = \ker(A\to A_\wp/\wp A_\wp)℘=ker(A→A℘/℘A℘) hold?
Always.
If and only if localization map A→A℘A\to A_\wpA→A℘ is injective.
If and only if ℘\wp℘ is a maximal ideal of AAA.
Hint please.
Type a concept, like “slope” or “photosynthesis”.