Theorems · Theorem · commutative algebra
IsAdjoinRootMonic.monic
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {f : Polynomial R}
(self : IsAdjoinRootMonic S f), f.Monic- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Monicstatement · cited by 461
- IsAdjoinRootMonicstatement and proof · cited by 35
Cited by5
Results whose statement or proof uses this declaration.
- IsAdjoinRootMonic.modByMonicHom_root_powproof · cited by 2
- IsAdjoinRootMonic.modByMonic_repr_mapproof · cited by 1
- IsAdjoinRootMonic.isIntegral_rootproof · cited by 1
- IsAdjoinRootMonic.coeff_apply_leproof · cited by 1
- IsAdjoinRootMonic.minpoly_eqproof · cited by 1