Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd
∀ {R : Type u_3} [inst : CommSemiring R] {p : Polynomial R},
Submodule.IsPrincipal p.contentIdeal → ∀ (r : R), p.contentIdeal ≤ Ideal.span {r} ↔ Polynomial.C r ∣ p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Polynomial.Cstatement and proof · cited by 1,598
- Ideal.spanstatement and proof · cited by 948
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.IsPrincipal.generatorproof · cited by 56
- map_dvdproof · cited by 44
- Polynomial.contentIdealstatement and proof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isPrimitive_of_contentIdeal_eq_topproof · cited by 1