Mathlib Map

Theorems · Definition · commutative algebra

ValuationSubring.toSubring

{K : Type u} → [inst : Field K] → ValuationSubring K → Subring K
Defined in
Mathlib.RingTheory.Valuation.ValuationSubring
Cited by
32 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
Field
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Around this declaration

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

ValuationSubring.pointwiseHasSMul · cited by 10ValuationSubring.pointwis…ValuationSubring.toLocalSubring · cited by 10ValuationSubring.toLocalS…Set.integer · cited by 8Set.integerValuation.exists_pow_Uniformizer · cited by 3Valuation.exists_pow_Unif…ValuationSubring.subtype · cited by 3ValuationSubring.subtypeValuationSubring.comap · cited by 3ValuationSubring.comapValuationSubring.isMax_toLocalSubring · cited by 2ValuationSubring.isMax_to…ValuationSubring.mem_or_inv_mem' · cited by 2ValuationSubring.mem_or_i…ValuationSubring.neg_mem · cited by 2ValuationSubring.neg_memValuationSubring.one_mem · cited by 2ValuationSubring.one_memIdeal.image_subset_nonunits_valuationSubring · cited by 2Ideal.image_subset_nonuni…ValuationSubring.zero_mem · cited by 2ValuationSubring.zero_memSubring.eq_iInf_of_isIntegrallyClosedIn · cited by 1Subring.eq_iInf_of_isInte…IsLocalRing.exists_factor_valuationRing · cited by 1IsLocalRing.exists_factor…Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn · cited by 1Subring.exists_le_valuati…Field · cited by 7404FieldSubring · cited by 602SubringValuationSubring · cited by 187ValuationSubringValuationSubring.toSubringCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by39

Results whose statement or proof uses this declaration.