Theorems · Theorem · commutative algebra
AdjoinRoot.adjoinRoot_eq_top
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R}, R[AdjoinRoot.root f] = ⊤- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 113 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Top.topstatement · cited by 9,680
- Polynomialstatement and proof · cited by 5,681
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- AdjoinRootstatement and proof · cited by 177
- AdjoinRoot.rootstatement and proof · cited by 77
- Algebra.eq_top_iffproof · cited by 13
- Algebra.adjoin_singleton_eq_range_aevalproof · cited by 12
- AdjoinRoot.aeval_eqproof · cited by 10
- AdjoinRoot.induction_onproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.adjoin_root_eq_top_of_isSplittingFieldproof · cited by 1
- IntermediateField.adjoin_root_eq_topproof · cited by 1
- Polynomial.SplittingFieldAux.adjoin_rootSetproof · cited by 0
- isSplittingField_AdjoinRoot_X_pow_sub_Cproof · cited by 0