Theorems · Definition · ring theory
Subalgebra.algEquivOpMop
{R : Type u_2} →
{A : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : Semiring A] → [inst_2 : Algebra R A] → (S : Subalgebra R A) → ↥S ≃ₐ[R] (↥S.op)ᵐᵒᵖBijection between a subalgebra S and MulOpposite of its opposite.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement and proof · cited by 1,353
- RingEquivproof · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- Subalgebra.toSubsemiringproof · cited by 115
- RingEquiv.toEquivproof · cited by 101
- Subsemiring.opproof · cited by 43
- Subalgebra.opstatement · cited by 30
- Subsemiring.ringEquivOpMopproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.algEquivOpMop_applystatement and proof · cited by 0
- Subalgebra.algEquivOpMop_symm_apply_coestatement and proof · cited by 0