Theorems · Definition · commutative algebra
AdjoinRoot.isAdjoinRoot
{R : Type u} → [inst : CommRing R] → (f : Polynomial R) → IsAdjoinRoot (AdjoinRoot f) fAdjoinRoot f is indeed given by adjoining a root of f.
- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 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.
Cites5
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
- Polynomialstatement and proof · cited by 5,681
- AdjoinRootstatement · cited by 177
- IsAdjoinRootstatement · cited by 61
- AdjoinRoot.mkₐproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- AdjoinRoot.isAdjoinRootMonicproof · cited by 3
- AdjoinRoot.isAdjoinRootMonic_toAdjoinRootstatement · cited by 1
- AdjoinRoot.isAdjoinRoot_root_eq_rootstatement · cited by 1
- AdjoinRoot.isAdjoinRoot_map_eq_mkₐstatement · cited by 0
- IsAdjoinRoot.ofAdjoinRootEquivproof · cited by 0