Theorems · Theorem · ring theory
RingHom.isUnit_map
∀ {α : Type u} {β : Type v} [inst : Semiring α] [inst_1 : Semiring β] (f : α →+* β) {a : α}, IsUnit a → IsUnit (f a)- Defined in
- Mathlib.Algebra.Ring.Units
- Cited by
- 14 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- IsUnitstatement · cited by 1,602
- IsUnit.mapproof · cited by 104
Cited by14
Results whose statement or proof uses this declaration.
- IsLocalRing.of_surjective'proof · cited by 3
- Polynomial.IsPrimitive.isUnit_iff_isUnit_map_of_injectiveproof · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpenproof · cited by 2
- Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeffproof · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpenproof · cited by 1
- Polynomial.degree_map_eq_of_isUnit_leadingCoeffproof · cited by 1
- Ring.ord_smul_of_isUnitproof · cited by 1
- AlgebraicGeometry.RingedSpace.basicOpen_of_isUnitproof · cited by 1
- IsLocalRing.of_surjectiveproof · cited by 1
- WittVector.irreducibleproof · cited by 0
- Polynomial.Monic.irreducible_of_irreducible_map_of_isPrime_nilradicalproof · cited by 0
- isLocalHom_of_compproof · cited by 0