Theorems · Definition · ring theory
AddMonoidAlgebra.opRingEquiv
{R : Type u_1} →
{M : Type u_2} → [inst : Semiring R] → [inst_1 : Add M] → (AddMonoidAlgebra R M)ᵐᵒᵖ ≃+* AddMonoidAlgebra Rᵐᵒᵖ MᵃᵒᵖThe opposite of a monoid algebra is equivalent as a ring to the opposite monoid algebra over the opposite ring.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Opposite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingEquivstatement · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- AddEquivproof · cited by 1,087
- AddMonoidAlgebrastatement and proof · cited by 649
- AddEquiv.symmproof · cited by 530
- AddOppositestatement and proof · cited by 452
- AddEquiv.toEquivproof · cited by 174
- AddEquiv.transproof · cited by 53
- MulOpposite.opAddEquivproof · cited by 25
- AddOpposite.opEquivproof · cited by 20
- AddMonoidAlgebra.mapAddEquivproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.opRingEquivproof · cited by 13
- AddMonoidAlgebra.opRingEquiv_applystatement and proof · cited by 3
- Polynomial.opRingEquiv_op_monomialproof · cited by 3
- Polynomial.coeff_opRingEquivproof · cited by 2
- AddMonoidAlgebra.opRingEquiv_symm_applystatement and proof · cited by 1
- AddMonoidAlgebra.opRingEquiv_singlestatement · cited by 0
- AddMonoidAlgebra.opRingEquiv_symm_singlestatement and proof · cited by 0