Theorems · Theorem · commutative algebra
IsAdjoinRoot.mem_ker_map
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRoot S f) {p : Polynomial R}, p ∈ RingHom.ker h.map ↔ f ∣ p- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- AlgHomstatement · cited by 3,236
- RingHom.kerstatement · cited by 363
- Ideal.mem_span_singletonproof · cited by 69
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.mapstatement · cited by 32
- IsAdjoinRoot.ker_mapproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsAdjoinRoot.map_eq_zero_iffproof · cited by 1
- IsAdjoinRootMonic.map_modByMonicproof · cited by 1
- IsAdjoinRootMonic.modByMonic_repr_mapproof · cited by 1