Theorems · Theorem · group theory
Localization.mk_zero
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {S : Submonoid M} (x : ↥S), Localization.mk 0 x = 0- Cited by
- 8 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidWithZerostatement and proof · cited by 913
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- OreLocalization.zero_oreDiv'proof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.val_zeroproof · cited by 6
- RatFunc.liftOn_mkproof · cited by 2
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_memproof · cited by 2
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.primeproof · cited by 0
- Localization.liftOn_zeroproof · cited by 0
- HomogeneousLocalization.mk_eq_zero_of_numproof · cited by 0