Theorems · Theorem · commutative algebra
AdjoinRoot.mk_eq_mk
∀ {R : Type u_1} [inst : CommRing R] {f g h : Polynomial R}, (AdjoinRoot.mk f) g = (AdjoinRoot.mk f) h ↔ f ∣ g - h- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AdjoinRootstatement · cited by 177
- Ideal.mem_span_singletonproof · cited by 69
- AdjoinRoot.mkstatement · cited by 50
- Ideal.Quotient.eqproof · cited by 22
Cited by6
Results whose statement or proof uses this declaration.
- AdjoinRoot.mk_eq_zeroproof · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.C_addPolynomialproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Yproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mulproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basisproof · cited by 0
- AdjoinRoot.mk_leftInverseproof · cited by 0