Theorems · Theorem · commutative algebra
IsAdjoinRootMonic.minpoly_eq
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {f : Polynomial R}
(h : IsAdjoinRootMonic S f) [IsDomain R] [IsDomain S] [Module.IsTorsionFree R S] [IsIntegrallyClosed R],
Irreducible f → minpoly R h.root = f- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Polynomialstatement and proof · cited by 5,681
- Monoidproof · cited by 3,887
- mul_oneproof · cited by 3,885
- IsDomainstatement and proof · cited by 2,196
- Module.IsTorsionFreestatement and proof · cited by 600
- Irreduciblestatement and proof · cited by 496
- minpolystatement and proof · cited by 439
- Associatedproof · cited by 296
- IsIntegrallyClosedstatement and proof · cited by 203
- minpoly.monicproof · cited by 81
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin.powerBasis'_minpoly_genproof · cited by 0