Theorems · Definition · commutative algebra
ValuativeRel.ValueGroupWithZero
(R : Type u_1) → [inst : Semiring R] → [ValuativeRel R] → Type u_1
The "canonical" value group-with-zero of a ring with a valuative relation.
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.valueSetoidproof · cited by 1
Cited by110
Results whose statement or proof uses this declaration.
- ValuativeRel.valuationstatement · cited by 42
- ValuativeRel.ValueGroupWithZero.mkstatement · cited by 25
- ValuativeRel.ValueGroupWithZero.orderMonoidIsostatement and proof · cited by 13
- ValuativeRel.ValueGroupWithZero.embedstatement and proof · cited by 7
- ValuativeRel.ValueGroupWithZero.indstatement and proof · cited by 6
- ValuativeRel.ValueGroupWithZero.liftstatement and proof · cited by 6
- ValuativeRel.uniformizerstatement · cited by 6
- Valuation.mem_nhds_iffproof · cited by 6
- ValuativeExtension.mapValueGroupWithZerostatement · cited by 5
- ValuativeRel.ValueGroupWithZero.embed_strictMonostatement and proof · cited by 4
- ValuativeRel.IsDiscrete.has_maximal_elementstatement · cited by 3
- ValuativeRel.IsNontrivial.casesOnstatement and proof · cited by 3