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Theorems · Definition · commutative algebra

ValuativeRel.trivialRel

{R : Type} → [inst : Semiring R] → [DecidableEq R] → [IsDomain R] → ValuativeRel R

The trivial valuative relation on a domain R, such that all non-zero elements are related. The domain condition is necessary so that the relation is closed when multiplying.

Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Trivial
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringDecidableEqIsDomain
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ValuativeRel.eq_trivialRel_of_compatible_one · cited by 1ValuativeRel.eq_trivialRe…ValuativeRel.trivialRel_eq_ofValuation_one · cited by 0ValuativeRel.trivialRel_e…Semiring · cited by 13802SemiringIsDomain · cited by 2196IsDomainValuativeRel · cited by 241ValuativeRelValuativeRel.trivialRelCITED BYCITES

Cites3

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Cited by2

Results whose statement or proof uses this declaration.