Theorems · Theorem · commutative algebra

Valuation.subgroups_basis

∀ {R : Type u} [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀),
  RingSubgroupsBasis fun γ => v.ltAddSubgroup ((Units.map ↑MonoidWithZeroHom.ValueGroup₀.embedding) γ)

The basis of open subgroups for the topology on a ring determined by a valuation.

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

5 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZero