Theorems · Theorem · commutative algebra
Ideal.mem_leadingCoeff
∀ {R : Type u} [inst : CommSemiring R] (I : Ideal (Polynomial R)) (x : R),
x ∈ I.leadingCoeff ↔ ∃ p ∈ I, p.leadingCoeff = x- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreeproof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.degree_le_natDegreeproof · cited by 14
- Ideal.leadingCoeffstatement · cited by 8
- Submodule.mem_iSup_of_directedproof · cited by 7
- Ideal.leadingCoeffNthproof · cited by 4
- Ideal.leadingCoeffNth_monoproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.leadingCoeff_mul_leproof · cited by 1
- Ideal.map_C_leadingCoeffproof · cited by 1
- Ideal.leadingCoeff_monoproof · cited by 0
- Ideal.map_C_comap_of_comap_eq_leadingCoeffproof · cited by 0