Theorems · Theorem · commutative algebra
AdjoinRoot.mk_surjective
∀ {R : Type u_1} [inst : CommRing R] {g : Polynomial R}, Function.Surjective ⇑(AdjoinRoot.mk g)- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 7 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.
Cites7
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.Quotient.mk_surjectiveproof · cited by 134
- AdjoinRoot.mkstatement · cited by 50
Cited by7
Results whose statement or proof uses this declaration.
- IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_mapstatement and proof · cited by 2
- StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_xproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdealproof · cited by 1
- IsAdjoinRoot.algEquiv_ofAlgEquivproof · cited by 0
- minpoly.ToAdjoin.injectiveproof · cited by 0
- mem_adjoin_map_integralClosure_of_isStandardEtaleproof · cited by 0
- IsAdjoinRoot.ofAlgEquiv_algEquivproof · cited by 0