Theorems · Theorem · commutative algebra
Ideal.exists_normalized_span_of_isPrincipal
∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : NormalizationMonoid R] (I : Ideal R) [Submodule.IsPrincipal I],
∃ x, normalize x = x ∧ I = Ideal.span {x}- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- le_antisymmproof · cited by 2,068
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.IsPrincipal.casesOnproof · cited by 15
- normalize_idemproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.exists_monic_spanproof · cited by 1