Theorems · Theorem · commutative algebra
IsFractionRing.isUnit_map_of_injective
∀ {A : Type u_4} [inst : CommRing A] {L : Type u_7} [inst_1 : Field L] {g : A →+* L},
Function.Injective ⇑g → ∀ (y : ↥(nonZeroDivisors A)), IsUnit (g ↑y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, 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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Submonoidstatement · cited by 3,086
- IsUnitstatement · cited by 1,602
- nonZeroDivisorsstatement and proof · cited by 895
- IsUnit.mk0proof · cited by 33
- RingHom.toMonoidWithZeroHomproof · cited by 24
- map_ne_zero_of_mem_nonZeroDivisorsproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- IsFractionRing.liftproof · cited by 12
- IsFractionRing.lift_algebraMapproof · cited by 6
- IsFractionRing.lift_uniqueproof · cited by 0