Theorems · Inductive type · commutative algebra

Valuation.Integers

{R : Type u} →
  {Γ₀ : Type v} →
    [inst : CommRing R] →
      [inst_1 : LinearOrderedCommGroupWithZero Γ₀] →
        Valuation R Γ₀ → (O : Type w) → [inst_2 : CommRing O] → [Algebra O R] → Prop

Given a valuation v : R → Γ₀ and a ring homomorphism O →+* R, we say that O is the integers of v if f is injective, and its range is exactly v.integer.

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

58 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CommRingLinearOrderedCommGroupWithZeroCommRingAlgebra