Theorems · Theorem · commutative algebra

ValuativeExtension.mapValueGroupWithZero_mk

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : ValuativeRel A]
  [inst_3 : ValuativeRel B] [inst_4 : Algebra A B] [inst_5 : ValuativeExtension A B] (r : A)
  (s : ↥(ValuativeRel.posSubmonoid A)),
  (ValuativeExtension.mapValueGroupWithZero A B) (ValuativeRel.ValueGroupWithZero.mk r s) =
    ValuativeRel.ValueGroupWithZero.mk ((algebraMap A B) r) ((ValuativeExtension.mapPosSubmonoid A B) s)

Defined in

Mathlib.RingTheory.Valuation.ValuativeRel.Basic

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingValuativeRelValuativeRelAlgebraValuativeExtension