Theorems · Definition · ring theory
AddMonoidAlgebra.single
{R : Type u_1} → {M : Type u_4} → [inst : Semiring R] → M → R → AddMonoidAlgebra R MAddMonoidAlgebra.single m r for m : M, r : R is the element rm : R[M].
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 250 results in Mathlib
- Foundations
- Depth 60 from the axioms, rests on 864 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Finsupp.singleproof · cited by 943
- AddMonoidAlgebrastatement · cited by 649
Cited by258
Results whose statement or proof uses this declaration.
- Polynomial.monomialproof · cited by 256
- LaurentPolynomial.Tproof · cited by 55
- Polynomial.coeff_C_mulproof · cited by 55
- MvPolynomial.rename_Xproof · cited by 48
- AddMonoidAlgebra.of'proof · cited by 25
- AddMonoidAlgebra.mapDomain_singlestatement and proof · cited by 23
- Polynomial.coeff_mul_Cproof · cited by 20
- AddMonoidAlgebra.single_mul_singlestatement and proof · cited by 20
- AddMonoidAlgebra.domCongr_singlestatement and proof · cited by 16
- MvPolynomial.induction_on'proof · cited by 15
- Polynomial.sum_monomial_eqproof · cited by 15
- AddMonoidAlgebra.coeff_mulproof · cited by 13
Showing the 200 most cited of 258.