Theorems · Definition · ring theory
AlgEquiv.moduleEndSelf
(R : Type u_1) →
{A : Type u_3} → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Aᵐᵒᵖ ≃ₐ[R] Module.End A AThe canonical algebra isomorphism from Aᵐᵒᵖ to Module.End A A induced by the right
multiplication.
- Defined in
- Mathlib.Algebra.Algebra.Opposite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingEquivproof · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- Module.Endstatement and proof · cited by 774
- RingEquiv.toEquivproof · cited by 101
- RingEquiv.moduleEndSelfproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- IsSimpleRing.exists_algEquiv_matrix_end_mulOppositeproof · cited by 2
- IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOppositeproof · cited by 2
- AlgEquiv.moduleEndSelf_apply_applystatement and proof · cited by 1
- IsAzumaya.tensorEquivEndproof · cited by 1
- AlgEquiv.moduleEndSelf_symm_applystatement and proof · cited by 0
- IsAzumaya.coe_tensorEquivEndproof · cited by 0
- matrixAlgEquivEndVecMulOppositeproof · cited by 0