Theorems · Theorem · commutative algebra
LocalSubring.exists_valuationRing_of_isMax
∀ {K : Type u_3} [inst : Field K] {R : LocalSubring K}, IsMax R → ∃ R', R'.toLocalSubring = R[Stacks Tag 00IB](https://stacks.math.columbia.edu/tag/00IB)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
- Subalgebraproof · cited by 1,353
- Polynomial.aevalproof · cited by 615
- Invertibleproof · cited by 549
- Algebra.adjoinproof · cited by 535
Cited by2
Results whose statement or proof uses this declaration.
- LocalSubring.exists_le_valuationSubringproof · cited by 2
- LocalSubring.isMax_iffproof · cited by 0