Theorems · Theorem · commutative algebra
map_mem_nonunits_iff
∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Monoid α] [inst_1 : Monoid β] [inst_2 : FunLike F α β]
[MonoidHomClass F α β] (f : F) [IsLocalHom f] (a : α), f a ∈ nonunits β ↔ a ∈ nonunits α- Defined in
- Mathlib.RingTheory.Ideal.Nonunits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
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
- Setstatement · cited by 53,352
- Monoidstatement and proof · cited by 3,887
- FunLikestatement and proof · cited by 2,560
- IsUnitproof · cited by 1,602
- MonoidHomClassstatement and proof · cited by 244
- IsUnit.mapproof · cited by 104
- IsLocalHomstatement and proof · cited by 100
- nonunitsstatement and proof · cited by 35
- IsUnit.of_mapproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.RingEquivClass.isDiscreteValuationRingproof · cited by 0