Theorems · Definition · commutative algebra

Valuation.leSubmodule

{R : Type u} →
  {Γ₀ : Type v} →
    [inst : Ring R] →
      [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → (v : Valuation R Γ₀) → Γ₀ → Submodule (↥v.integer) R

The v.integer-submodule of R of elements whose valuation is less than or equal to a certain value.

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

7 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZero