Theorems · Theorem · commutative algebra
map_ne_zero_of_mem_nonZeroDivisors
∀ {F : Type u_1} {M₀ : Type u_2} {M₀' : Type u_3} [inst : MonoidWithZero M₀] [inst_1 : MonoidWithZero M₀']
[inst_2 : FunLike F M₀ M₀'] [Nontrivial M₀] [ZeroHomClass F M₀ M₀'] (g : F),
Function.Injective ⇑g → ∀ {x : M₀}, x ∈ nonZeroDivisors M₀ → g x ≠ 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Submonoidstatement · cited by 3,086
- one_mulproof · cited by 2,841
- FunLikestatement and proof · cited by 2,560
- Nontrivialstatement and proof · cited by 2,416
- map_zeroproof · cited by 1,614
- nonZeroDivisorsstatement and proof · cited by 895
- one_ne_zeroproof · cited by 885
- MonoidWithZerostatement and proof · cited by 456
- ZeroHomClassstatement and proof · cited by 74
Cited by6
Results whose statement or proof uses this declaration.
- IsBaseChange.lift_rank_eqproof · cited by 3
- IsFractionRing.isUnit_map_of_injectiveproof · cited by 2
- RatFunc.liftMonoidWithZeroHom_injectiveproof · cited by 2
- map_mem_nonZeroDivisorsproof · cited by 1
- Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroproof · cited by 1