Theorems · Theorem · ring theory
RingHomInvPair.of_ringEquiv
∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] (e : R₁ ≃+* R₂), RingHomInvPair ↑e ↑e.symmConstruct a RingHomInvPair from both directions of a ring equiv.
This is not an instance, as for equivalences that are involutions, a better instance
would be RingHomInvPair e e.
- Defined in
- Mathlib.Algebra.Ring.CompTypeclasses
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingEquivstatement and proof · cited by 1,147
- RingHomClass.toRingHomstatement · cited by 746
- RingEquiv.symmstatement and proof · cited by 567
- RingHomInvPairstatement · cited by 523
- RingEquiv.symm_toRingHom_comp_toRingHomproof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- RingEquiv.isSemisimpleRingproof · cited by 6
- RingEquiv.toSemilinearEquivstatement · cited by 6
- RingHom.LocalizationAwayPreserves.respectsIsoproof · cited by 4
- ModuleCat.hasProjectiveDimensionLE_of_semiLinearEquivstatement · cited by 3
- ModuleCat.projectiveDimension_eq_of_semiLinearEquivstatement · cited by 2
- ModuleCat.injectiveDimension_eq_of_semiLinearEquivstatement · cited by 1
- ModuleCat.hasInjectiveDimensionLE_iff_of_semiLinearEquivstatement · cited by 1
- Module.Injective.of_ringEquivstatement · cited by 1
- RingEquiv.toSemilinearEquiv_applystatement · cited by 1
- RingEquiv.toSemilinearEquiv_symm_applystatement · cited by 1
- RingEquiv.symm_toSemilinearEquiv_symm_applystatement · cited by 0
- RingHomInvPair.of_ringEquiv_symmproof · cited by 0