Theorems · Theorem · field theory
IsAlgebraic.exists_nonzero_eq_adjoin_mul
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] {s : S},
IsAlgebraic R s → s ∈ nonZeroDivisors S → ∃ t ∈ R[s], ∃ r, r ≠ 0 ∧ s * t = (algebraMap R S) r- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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 · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomproof · cited by 3,236
- Submonoidstatement · cited by 3,086
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgebraic.of_mulproof · cited by 4