Theorems · Theorem · commutative algebra

Module.support_quotient

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Finite R M]
  (I : Ideal R), Module.support R (M ⧸ I • ⊤) = Module.support R M ∩ PrimeSpectrum.zeroLocus ↑I

Supp(M/IM) = Supp(M) ∩ Z(I).

Defined in

Mathlib.RingTheory.Support

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.Finite