Theorems · Theorem · field theory
IsAlgebraic.exists_nonzero_dvd
∀ {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 → ∃ r, r ≠ 0 ∧ s ∣ (algebraMap R S) r- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 5 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.
Cites22
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
- 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 · cited by 4,706
- Submonoidstatement · cited by 3,086
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- nonZeroDivisorsstatement and proof · cited by 895
Cited by5
Results whose statement or proof uses this declaration.
- IsAlgebraic.restrictScalars_of_isIntegralproof · cited by 4
- IsAlgebraic.exists_smul_eq_mulproof · cited by 3
- Algebra.IsAlgebraic.injective_tower_topproof · cited by 2
- MvPolynomial.exists_dvd_map_of_isAlgebraicproof · cited by 0
- Polynomial.exists_dvd_map_of_isAlgebraicproof · cited by 0