Theorems · Theorem · ring theory
MonoidAlgebra.ext
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {x y : MonoidAlgebra R M}, x.coeff = y.coeff → x = yAlias of the forward direction of MonoidAlgebra.coeff_inj.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finsuppstatement · cited by 5,255
- MonoidAlgebrastatement and proof · cited by 590
- MonoidAlgebra.coeffstatement · cited by 224
- MonoidAlgebra.coeff_injproof · cited by 2
Cited by78
Results whose statement or proof uses this declaration.
- MonoidAlgebra.mapDomain_singleproof · cited by 12
- MonoidAlgebra.smul_singleproof · cited by 10
- MonoidAlgebra.tensorEquiv_single_tmul_singleproof · cited by 8
- MonoidAlgebra.sum_coeff_singleproof · cited by 6
- MonoidAlgebra.mapAlgHom_singleproof · cited by 3
- MonoidAlgebra.map_singleproof · cited by 3
- MonoidAlgebra.mapDomainBialgHom_compproof · cited by 2
- MonoidAlgebra.uniqueRingEquiv_symm_applyproof · cited by 2
- MonoidAlgebra.mapRingHom_compproof · cited by 2
- MonoidAlgebra.ext_iffproof · cited by 2
- Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_subproof · cited by 1
- MonoidAlgebra.mapAddEquiv_transproof · cited by 1