Theorems · Theorem · field theory
isAlgebraic_zero
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [Nontrivial R], IsAlgebraic R 0- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- IsAlgebraicstatement · cited by 163
- Polynomial.aeval_Xproof · cited by 120
- Polynomial.X_ne_zeroproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.isAlgebraicproof · cited by 2
- IsIntegral.trans_isAlgebraicproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1