Theorems · Theorem · commutative algebra
Polynomial.mem_closure_X_union_C
∀ {R : Type u_1} [inst : Ring R] (p : Polynomial R), p ∈ Subring.closure (insert Polynomial.X {f | f.degree ≤ 0})- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Ringstatement and proof · cited by 7,463
- Set.ofPredstatement and proof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Subringstatement · cited by 602
- pow_succproof · cited by 374
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isIntegral_isLocalization_polynomial_quotientproof · cited by 1