Theorems · Theorem · commutative algebra
WithVal.algebraMap_right_injective
∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {S : Type u_3} [inst_1 : CommSemiring R]
[inst_2 : Ring S] [inst_3 : Algebra R S] (v : Valuation S Γ₀),
Function.Injective ⇑(algebraMap R S) → Function.Injective ⇑(algebraMap R (WithVal v))- Defined in
- Mathlib.Topology.Algebra.Valued.WithVal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- WithValstatement · cited by 151
- WithVal.toVal_injectiveproof · cited by 3
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