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Theorems · Definition · ring theory

RingEquiv.toOpposite

(R : Type u_4) → [inst : NonUnitalCommSemiring R] → R ≃+* Rᵐᵒᵖ

A non-unital commutative ring is isomorphic to its opposite.

Defined in
Mathlib.Algebra.Ring.Equiv
Cited by
3 results in Mathlib
Foundations
Depth 22 from the axioms · uses Quot.sound
Assumes
NonUnitalCommSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgEquiv.toOpposite · cited by 6AlgEquiv.toOppositeAlgEquiv.toRingEquiv_toOpposite · cited by 0AlgEquiv.toRingEquiv_toOp…RingInvo.id · cited by 0RingInvo.idRingEquiv.toOpposite_apply · cited by 0RingEquiv.toOpposite_applyRingEquiv.toOpposite_symm_apply · cited by 0RingEquiv.toOpposite_symm…Equiv · cited by 8337EquivRingEquiv · cited by 1147RingEquivMulOpposite · cited by 1135MulOppositeNonUnitalCommSemiring · cited by 29NonUnitalCommSemiringMulOpposite.opEquiv · cited by 24MulOpposite.opEquivRingEquiv.toOppositeCITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.