Integral extension implies inverse image of max-spectrum is max-spectrum
This article gives the statement, and possibly proof, of a fact about how a property of a homomorphism of commutative unital rings, forces a property for the induced map on spectra
View other facts about induced maps on spectra
Then the following are true:
- If is a maximal ideal of , then is maximal in
- If is maximal in , then is maximal in
The key idea here is the following fact: for a finite extension of integral domains, one of them is a field if and only if the other is.