Theorems · Theorem · ring theory
SkewMonoidAlgebra.single_mul_single
∀ {k : Type u_1} {G : Type u_2} [inst : Semiring k] [inst_1 : Monoid G] [inst_2 : MulSemiringAction G k] {a₁ a₂ : G}
{b₁ b₂ : k},
SkewMonoidAlgebra.single a₁ b₁ * SkewMonoidAlgebra.single a₂ b₂ = SkewMonoidAlgebra.single (a₁ * a₂) (b₁ * a₁ • b₂)- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- smul_zeroproof · cited by 665
- MulSemiringActionstatement and proof · cited by 423
- SkewMonoidAlgebrastatement · cited by 216
- SkewMonoidAlgebra.singlestatement and proof · cited by 83
- SkewMonoidAlgebra.sumproof · cited by 46
- SkewMonoidAlgebra.sum_single_indexproof · cited by 12
- SkewMonoidAlgebra.single_zeroproof · cited by 8
- SkewMonoidAlgebra.sum_zeroproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- SkewPolynomial.monomial_mul_monomialproof · cited by 5
- SkewMonoidAlgebra.ringHom_extproof · cited by 1
- SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_ofproof · cited by 0
- SkewMonoidAlgebra.single_eq_algebraMap_mul_ofproof · cited by 0