Theorems · Theorem · commutative algebra

map_le_nonZeroDivisors_of_injective

∀ {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'] [NoZeroDivisors M₀'] [inst_4 : MonoidWithZeroHomClass F M₀ M₀'] (f : F),
  Function.Injective ⇑f → ∀ {S : Submonoid M₀}, S ≤ nonZeroDivisors M₀ → Submonoid.map f S ≤ nonZeroDivisors M₀'

Defined in

Mathlib.Algebra.GroupWithZero.NonZeroDivisors

Cited by

5 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidWithZeroMonoidWithZeroFunLikeNoZeroDivisorsMonoidWithZeroHomClass