Theorems · Theorem · ring theory

GradedAlgHom.map_mem

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} {ι : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : DecidableEq ι] [inst_6 : AddMonoid ι]
  {𝒜 : ι → Submodule R A} {ℬ : ι → Submodule R B} [inst_7 : GradedAlgebra 𝒜] [inst_8 : GradedAlgebra ℬ]
  (self : 𝒜 →ₐᵍ[R] ℬ) {i : ι} {x : A}, x ∈ 𝒜 i → (↑self).toRingHom x ∈ ℬ i

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraDecidableEqAddMonoidGradedAlgebraGradedAlgebra