Theorems · Theorem · commutative algebra
IsAdjoinRootMonic.isIntegral_root
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRootMonic S f), IsIntegral R h.root- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsIntegralstatement · cited by 427
- IsAdjoinRootMonicstatement and proof · cited by 35
- IsAdjoinRoot.rootstatement · cited by 34
- IsAdjoinRootMonic.toIsAdjoinRootstatement and proof · cited by 18
- IsAdjoinRootMonic.monicproof · cited by 5
- IsAdjoinRoot.aeval_root_selfproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsAdjoinRootMonic.minpoly_eqproof · cited by 1