Theorems · Definition · ring theory
MonoidAlgebra.uniqueRingEquiv
{R : Type u_1} → (M : Type u_4) → [inst : Semiring R] → [inst_1 : Monoid M] → [Subsingleton M] → MonoidAlgebra R M ≃+* RThe trivial monoid algebra is the base ring.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMonoidSubsingleton
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
- Monoidstatement and proof · cited by 3,887
- RingEquivstatement · cited by 1,147
- AddEquivproof · cited by 1,087
- MonoidAlgebrastatement and proof · cited by 590
- AddEquiv.toEquivproof · cited by 174
- AddEquiv.transproof · cited by 53
- MonoidAlgebra.coeffAddEquivproof · cited by 11
- Finsupp.uniqueAddEquivproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- MonoidAlgebra.uniqueAlgEquivproof · cited by 5
- MonoidAlgebra.uniqueRingEquiv_symm_applystatement · cited by 2
- MonoidAlgebra.coeff_uniqueRingEquiv_symmstatement · cited by 1
- MonoidAlgebra.uniqueRingEquiv_applystatement and proof · cited by 0
- MonoidAlgebra.uniqueRingEquiv_symm_apply_applystatement · cited by 0
- MonoidAlgebra.uniqueRingEquiv.congr_simpstatement and proof · cited by 0
- MonoidAlgebra.toRingEquiv_symm_uniqueAlgEquivstatement · cited by 0
- MonoidAlgebra.toRingEquiv_uniqueAlgEquivstatement · cited by 0