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Theorems · Theorem · commutative algebra

Valuation.mem_supp_iff

∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : CommRing R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
  (x : R), x ∈ v.supp ↔ v x = 0
Defined in
Mathlib.RingTheory.Valuation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext
Assumes
CommRingLinearOrderedCommMonoidWithZero
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Around this declaration

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

Valuation.comap_supp · cited by 2Valuation.comap_suppAddValuation.mem_supp_iff · cited by 0AddValuation.mem_supp_iffDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingIdeal · cited by 4748IdealValuation · cited by 823ValuationLinearOrderedCommMonoidWithZero · cited by 139LinearOrderedCommMonoidWi…Valuation.supp · cited by 12Valuation.suppValuation.mem_supp_iffCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.