Commutative algebra

Serre's inequality on height

In algebra, specifically in the theory of commutative rings, Serre's inequality on height states: given a (Noetherian) regular ring A and a pair of prime ideals in it, for each prime ideal that is a minimal prime ideal over the sum , the following inequality on heights holds: Without the assumption on regularity, the inequality can fail; see scheme-theoretic intersection#Proper intersection. (Wikipedia).

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Related pages

Prime ideal | Scheme-theoretic intersection | Minimal prime ideal | Serre's multiplicity conjectures | Regular ring | Discrete valuation ring | Commutative ring