Theorems · Theorem · commutative algebra
Ideal.image_subset_nonunits_valuationSubring
∀ {K : Type u_3} [inst : Field K] {A : Subring K} (I : Ideal ↥A),
I ≠ ⊤ → ∃ B, A ≤ B.toSubring ∧ ⇑A.subtype '' ↑I ⊆ ↑B.nonunits- Cited by
- 2 results in Mathlib
- Foundations
- Depth 141 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.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHomstatement · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- RingHom.compproof · cited by 899
- Ideal.mapproof · cited by 692
Cited by2
Results whose statement or proof uses this declaration.
- Subring.exists_le_valuationSubring_of_isIntegrallyClosedInproof · cited by 1
- LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedInproof · cited by 1