Theorems · Definition · ring theory
RingEquiv.refl
(R : Type u_4) → [inst : Mul R] → [inst_1 : Add R] → R ≃+* R
The identity map is a ring isomorphism.
- Defined in
- Mathlib.Algebra.Ring.Equiv
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingEquivstatement · cited by 1,147
- MulEquivproof · cited by 1,142
- AddEquivproof · cited by 1,087
- MulEquiv.toEquivproof · cited by 126
- AddEquiv.reflproof · cited by 34
- MulEquiv.reflproof · cited by 33
- AddEquiv.map_add'proof · cited by 5
- MulEquiv.map_mul'proof · cited by 1
Cited by89
Results whose statement or proof uses this declaration.
- AlgEquiv.reflproof · cited by 50
- IsLocalization.algEquivproof · cited by 45
- ZMod.ringEquivCongrproof · cited by 11
- commAlgCatEquivUnderproof · cited by 9
- OrderRingIso.reflproof · cited by 9
- Rat.HeightOneSpectrum.adicCompletion.padicEquivproof · cited by 5
- IsLocalization.algEquiv_applystatement · cited by 5
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivproof · cited by 4
- FractionalIdeal.canonicalEquiv_selfstatement and proof · cited by 4
- Valuation.IsEquiv.orderRingIsoproof · cited by 4
- ClassGroup.mk_eq_one_iffproof · cited by 4
- PerfectRing.lift_comp_applyproof · cited by 3