Theorems · Theorem · group theory
MonoidWithZeroHom.valueMonoid_eq_closure
∀ {A : Type u_1} {B : Type u_2} [inst : MonoidWithZero A] [inst_1 : MonoidWithZero B] (f : A →*₀ B),
f.valueMonoid = Submonoid.closure (Units.val ⁻¹' Set.range ⇑f)- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZeroMonoidWithZero
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Set.preimagestatement · cited by 4,946
- Set.rangestatement · cited by 4,705
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- Units.valstatement · cited by 1,966
- MonoidWithZeroHomstatement and proof · cited by 704
- MonoidWithZerostatement and proof · cited by 456
- Submonoid.closurestatement · cited by 167
- Submonoid.closure_eqproof · cited by 13
- MonoidWithZeroHom.valueMonoidstatement and proof · cited by 10
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