Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.embed_mk
∀ {R : Type u_2} {Γ : Type u_3} [inst : Ring R] [inst_1 : ValuativeRel R] [inst_2 : LinearOrderedCommGroupWithZero Γ]
(v : Valuation R Γ) [inst_3 : v.Compatible] (x : R) (s : ↥(ValuativeRel.posSubmonoid R)),
(ValuativeRel.ValueGroupWithZero.embed v) (ValuativeRel.ValueGroupWithZero.mk x s) =
(MonoidWithZeroHom.ValueGroup₀.restrict₀ (MonoidWithZeroHom.ofClass v)) x /
(MonoidWithZeroHom.ValueGroup₀.restrict₀ (MonoidWithZeroHom.ofClass v)) ↑sThe element .mk x s in ValueGroupWithZero R is sent to v x / v s in the
image group of v.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- Valuationstatement and proof · cited by 823
- MonoidWithZeroHomstatement · cited by 704
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- ValuativeRelstatement and proof · cited by 241
- MonoidWithZeroHom.ofClassstatement · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement · cited by 166
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀proof · cited by 2