Theorems · Theorem · algebraic geometry

Module.freeLocus_eq_univ

∀ {R : Type uR} {M : Type uM} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Finite R M]
  [Module.Flat R M], Module.freeLocus R M = Set.univ

Defined in: Mathlib.RingTheory.Spectrum.Prime.FreeLocus
Cited by: 1 results in Mathlib
Foundations: Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.Finite Module.Flat

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Set.univstatement · cited by 3,945
Module.Finitestatement and proof · cited by 1,032
PrimeSpectrumstatement and proof · cited by 625
Module.Flatstatement and proof · cited by 279
Module.freeLocusstatement · cited by 15
Module.free_of_flat_of_isLocalRingproof · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

Module.isLocallyConstant_rankAtStalkproof · cited by 1