Theorems · Theorem · commutative algebra
Module.support_eq_empty_iff
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],
Module.support R M = ∅ ↔ Subsingleton M- Defined in
- Mathlib.RingTheory.Support
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- one_smulproof · cited by 1,374
- PrimeSpectrumstatement and proof · cited by 625
- Submonoid.powersproof · cited by 408
- Module.supportstatement and proof · cited by 52
- Set.subset_empty_iffproof · cited by 40
- Submonoid.powers_oneproof · cited by 7
- LocalizedModule.subsingleton_iff_support_subsetproof · cited by 5
- LocalizedModule.subsingleton_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Module.nonempty_support_iffproof · cited by 2
- Algebra.etaleLocus_eq_univ_iffproof · cited by 1
- Algebra.unramifiedLocus_eq_univ_iffproof · cited by 1
- Module.rankAtStalk_eq_zero_iff_subsingletonproof · cited by 0
- Module.support_eq_emptyproof · cited by 0