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Theorems · Theorem · ring theory

SkewMonoidAlgebra.mul_def

∀ {k : Type u_1} {G : Type u_2} [inst : Mul G] [inst_1 : SMul G k] [inst_2 : NonUnitalNonAssocSemiring k]
  {f g : SkewMonoidAlgebra k G},
  f * g = f.sum fun a₁ b₁ => g.sum fun a₂ b₂ => SkewMonoidAlgebra.single (a₁ * a₂) (b₁ * a₁ • b₂)
Defined in
Mathlib.Algebra.SkewMonoidAlgebra.Basic
Cited by
2 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulSMulNonUnitalNonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SkewMonoidAlgebra.coeff_mul · cited by 9SkewMonoidAlgebra.coeff_m…SkewMonoidAlgebra.mapDomain_mul · cited by 0SkewMonoidAlgebra.mapDoma…NonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringSkewMonoidAlgebra · cited by 216SkewMonoidAlgebraSkewMonoidAlgebra.single · cited by 83SkewMonoidAlgebra.singleSkewMonoidAlgebra.sum · cited by 46SkewMonoidAlgebra.sumSkewMonoidAlgebra.mul_defCITED BYCITES

Cites4

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Cited by2

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