Theorems · Theorem · field theory
Algebra.IsAlgebraic.isDomain_of_adjoin_range
∀ (R : Type u_1) {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (s : Set A)
[NoZeroDivisors A] [Algebra.IsAlgebraic (↥(Algebra.adjoin R s)) A], IsDomain A- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Nontrivialproof · cited by 2,416
- IsDomainstatement · cited by 2,196
- Subalgebrastatement · cited by 1,353
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.adjoinstatement and proof · cited by 535
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Subtype.val_injectiveproof · cited by 232
- Function.Injective.nontrivialproof · cited by 17
- isDomain_iff_noZeroDivisors_and_nontrivialproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2
- Algebra.IsAlgebraic.trdeg_le_cardinalMkproof · cited by 1