Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.isPrimitive_iff_contentIdeal_eq_top
∀ {R : Type u_3} [inst : CommSemiring R] {p : Polynomial R},
Submodule.IsPrincipal p.contentIdeal → (p.IsPrimitive ↔ p.contentIdeal = ⊤)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 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
- Top.topstatement and proof · cited by 9,680
- Polynomialstatement and proof · cited by 5,681
- Idealstatement · cited by 4,748
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.IsPrincipal.generatorproof · cited by 56
- Polynomial.IsPrimitivestatement · cited by 33
- Polynomial.contentIdealstatement and proof · cited by 24
- Ideal.span_singleton_generatorproof · cited by 17
- Submodule.IsPrincipal.contentIdeal_generator_dvdproof · cited by 2
- Polynomial.isPrimitive_of_contentIdeal_eq_topproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isPrimitive_iff_contentIdeal_eq_topproof · cited by 1