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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.symm

Construct 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
Assumes
SemiringSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingEquiv.isSemisimpleRing · cited by 6RingEquiv.isSemisimpleRingRingEquiv.toSemilinearEquiv · cited by 6RingEquiv.toSemilinearEqu…RingHom.LocalizationAwayPreserves.respectsIso · cited by 4LocalizationAwayPreserves…ModuleCat.hasProjectiveDimensionLE_of_semiLinearEquiv · cited by 3ModuleCat.hasProjectiveDi…ModuleCat.projectiveDimension_eq_of_semiLinearEquiv · cited by 2ModuleCat.projectiveDimen…ModuleCat.injectiveDimension_eq_of_semiLinearEquiv · cited by 1ModuleCat.injectiveDimens…ModuleCat.hasInjectiveDimensionLE_iff_of_semiLinearEquiv · cited by 1ModuleCat.hasInjectiveDim…Module.Injective.of_ringEquiv · cited by 1Injective.of_ringEquivRingEquiv.toSemilinearEquiv_apply · cited by 1RingEquiv.toSemilinearEqu…RingEquiv.toSemilinearEquiv_symm_apply · cited by 1RingEquiv.toSemilinearEqu…RingEquiv.symm_toSemilinearEquiv_symm_apply · cited by 0RingEquiv.symm_toSemiline…RingHomInvPair.of_ringEquiv_symm · cited by 0RingHomInvPair.of_ringEqu…CategoryTheory.projectiveDimension_eq_of_semiLinearEquiv · cited by 0CategoryTheory.projective…RingEquiv.isIntegral_iff · cited by 0RingEquiv.isIntegral_iffCategoryTheory.hasProjectiveDimensionLE_of_semiLinearEquiv · cited by 0CategoryTheory.hasProject…Semiring · cited by 13802SemiringRingEquiv · cited by 1147RingEquivRingHomClass.toRingHom · cited by 746RingHomClass.toRingHomRingEquiv.symm · cited by 567RingEquiv.symmRingHomInvPair · cited by 523RingHomInvPairRingEquiv.symm_toRingHom_comp_toRingHom · cited by 3RingEquiv.symm_toRingHom_…RingHomInvPair.of_ringEquivCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.