Theorems · Theorem · commutative algebra

HomogeneousLocalization.val_pow

∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A]
  [inst_2 : AddSubgroupClass σ A] [inst_3 : AddCommMonoid ι] [inst_4 : DecidableEq ι] {𝒜 : ι → σ}
  [inst_5 : GradedRing 𝒜] {x : Submonoid A} (y : HomogeneousLocalization 𝒜 x) (n : ℕ), (y ^ n).val = y.val ^ n

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

4 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRing