Theorems · Definition · commutative algebra

Algebra.QuasiFiniteAt

(R : Type u_1) →
  {S : Type u_2} → [inst : CommRing R] → [inst_1 : CommRing S] → [Algebra R S] → (p : Ideal S) → [p.IsPrime] → Prop

If S is an R-algebra and p a prime of S, we say that S is R-quasi-finite at p if Sₚ is R-quasi-finite. In the case where S is (essentially) of finite type over R, this is equivalent to the usual definition that p is isolated in its fiber. See Ideal.exists_notMem_forall_mem_of_ne_of_liesOver.

Defined in

Mathlib.RingTheory.QuasiFinite.Basic

Cited by

29 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.IsPrime