Theorems · Theorem · field theory
Algebra.IsAlgebraic.nontrivial
∀ (R : Type u) (A : Type v) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [alg : Algebra.IsAlgebraic R A], Nontrivial R
- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement · cited by 2,416
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Algebra.IsAlgebraic.isAlgebraicproof · cited by 51
- IsAlgebraic.nontrivialproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.extendScalarsproof · cited by 4
- Algebra.IsAlgebraic.isDomain_of_adjoin_rangeproof · cited by 2
- Algebra.IsAlgebraic.exists_integral_multiplesproof · cited by 2
- exists_isTranscendenceBasis_betweenproof · cited by 1
- IsIntegral.trans_isAlgebraicproof · cited by 1