Theorem of transition

In algebra, the theorem of transition is said to hold between commutative rings if

1. dominates ; i.e., for each proper ideal I of A, is proper and for each maximal ideal of B, is maximal
2. for each maximal ideal and -primary ideal of , is finite and moreover
3. :

Given commutative rings such that dominates and for each maximal ideal of such that is finite, the natural inclusion is a faithfully flat ring homomorphism if and only if the theorem of transition holds between .

Notes

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