Theorems · Theorem · commutative algebra
Ideal.singleton_span_mem_normalizedFactors_of_mem_normalizedFactors
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsPrincipalIdealRing R]
[inst_3 : NormalizationMonoid R] {a b : R},
a ∈ UniqueFactorizationMonoid.normalizedFactors b →
Ideal.span {a} ∈ UniqueFactorizationMonoid.normalizedFactors (Ideal.span {b})- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanstatement and proof · cited by 948
- Associatedproof · cited by 296
- Primeproof · cited by 277
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- IsPrincipalIdealRingstatement and proof · cited by 131
Cited by1
Results whose statement or proof uses this declaration.
- singleton_span_mem_normalizedFactors_of_mem_normalizedFactorsproof · cited by 0