Theorems · Theorem · commutative algebra
Polynomial.monic_toSubring
∀ {R : Type u_1} [inst : Ring R] (p : Polynomial R) (T : Subring R) (hp : ↑p.coeffs ⊆ ↑T),
(p.toSubring T hp).Monic ↔ p.Monic- Defined in
- Mathlib.RingTheory.Polynomial.Subring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Subringstatement and proof · cited by 602
- Polynomial.Monicstatement · cited by 461
- Subtype.coe_injectiveproof · cited by 205
- Polynomial.coeffsstatement and proof · cited by 41
- Polynomial.toSubringstatement and proof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- isIntegral_transproof · cited by 15
- FixedPoints.minpoly.monicproof · cited by 4
- IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_elementproof · cited by 1