Theorems · Theorem · commutative algebra
Module.mem_support_iff
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{p : PrimeSpectrum R}, p ∈ Module.support R M ↔ Nontrivial (LocalizedModule p.asIdeal.primeCompl M)- Defined in
- Mathlib.RingTheory.Support
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Nontrivialstatement · cited by 2,416
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplstatement · cited by 462
- PrimeSpectrum.asIdealstatement · cited by 333
- LocalizedModulestatement · cited by 154
- Module.supportstatement · cited by 52
Cited by3
Results whose statement or proof uses this declaration.
- Module.support_quotientproof · cited by 1
- Module.mem_support_iff_nontrivial_residueField_tensorProductproof · cited by 0