Theorems · Definition · ring theory
MonoidAlgebra.uniqueAlgEquiv
(R : Type u_1) →
{A : Type u_4} →
(M : Type u_7) →
[inst : CommSemiring R] →
[inst_1 : Semiring A] →
[inst_2 : Algebra R A] → [inst_3 : Monoid M] → [Subsingleton M] → MonoidAlgebra A M ≃ₐ[R] AThe trivial monoid algebra is the base ring.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Monoidstatement and proof · cited by 3,887
- AlgEquivstatement · cited by 1,681
- RingEquivproof · cited by 1,147
- MonoidAlgebrastatement and proof · cited by 590
- RingEquiv.toEquivproof · cited by 101
- MonoidAlgebra.uniqueRingEquivproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- MonoidAlgebra.uniqueAlgEquiv_symm_applystatement · cited by 1
- MonoidAlgebra.toRingEquiv_symm_uniqueAlgEquivstatement · cited by 0
- MonoidAlgebra.toRingEquiv_uniqueAlgEquivstatement · cited by 0
- MonoidAlgebra.uniqueAlgEquiv.congr_simpstatement and proof · cited by 0
- MonoidAlgebra.coeff_uniqueAlgEquiv_symmstatement · cited by 0