Theorems · Theorem · commutative algebra
IsAdjoinRoot.isAlgebraic_root
∀ {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), f ≠ 0 → IsAlgebraic R h.root- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- IsAlgebraicstatement · cited by 163
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.rootstatement · cited by 34
- IsAdjoinRoot.aeval_root_eq_mapproof · cited by 5
- IsAdjoinRoot.map_selfproof · cited by 2
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