Theorems · Definition · ring theory
RingEquiv.opOp
(R : Type u_7) → [inst : Add R] → [inst_1 : Mul R] → R ≃+* Rᵐᵒᵖᵐᵒᵖ
A ring is isomorphic to the opposite of its opposite.
- Defined in
- Mathlib.Algebra.Ring.Equiv
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses Quot.sound
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.
- RingEquivstatement · cited by 1,147
- MulEquivproof · cited by 1,142
- MulOppositestatement and proof · cited by 1,135
- MulEquiv.toEquivproof · cited by 126
- MulEquiv.opOpproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- AlgEquiv.opOpproof · cited by 5
- IsSimpleRing.exists_ringEquiv_matrix_end_mulOppositeproof · cited by 1
- NormedSpace.exp_opproof · cited by 1
- RingEquiv.opOp_applystatement and proof · cited by 0
- RingEquiv.opOp_symm_applystatement and proof · cited by 0
- AlgEquiv.toRingEquiv_opOpstatement · cited by 0
- isSemisimpleRing_mulOpposite_iffproof · cited by 0