Theorems · Theorem · commutative algebra
LocalizedModule.subsingleton_iff_support_subset
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {f : R},
Subsingleton (LocalizedModule.Away f M) ↔ Module.support R M ⊆ PrimeSpectrum.zeroLocus {f}- Defined in
- Mathlib.RingTheory.Support
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 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.
Cites26
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
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Idealproof · cited by 4,748
- Submodule.spanproof · cited by 1,504
- one_smulproof · cited by 1,374
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- Submonoid.powersproof · cited by 408
Cited by5
Results whose statement or proof uses this declaration.
- Module.support_eq_empty_iffproof · cited by 5
- Algebra.basicOpen_subset_etaleLocus_iffproof · cited by 3
- Algebra.basicOpen_subset_smoothLocus_iffproof · cited by 3
- Algebra.basicOpen_subset_unramifiedLocus_iffproof · cited by 3
- LocalizedModule.subsingleton_iff_disjointproof · cited by 0