Theorems · Theorem · commutative algebra
AdjoinRoot.mk_eq_zero
∀ {R : Type u_1} [inst : CommRing R] {f g : Polynomial R}, (AdjoinRoot.mk f) g = 0 ↔ f ∣ g- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- sub_zeroproof · cited by 938
- AdjoinRootstatement · cited by 177
- AdjoinRoot.mkstatement · cited by 50
- AdjoinRoot.mk_eq_mkproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- AdjoinRoot.mk_ne_zero_of_natDegree_ltproof · cited by 4
- AdjoinRoot.minpoly_rootproof · cited by 3
- AdjoinRoot.of.injective_of_degree_ne_zeroproof · cited by 1
- AdjoinRoot.mk_ne_zero_of_degree_ltproof · cited by 0