Theorems · Theorem · commutative algebra
IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipal
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [IsGCDMonoid R] {J : Ideal R},
(∃ K, J * K ≠ 0 ∧ Submodule.IsPrincipal (J * K)) → Submodule.IsPrincipal J- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainIsGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- Submodule.spanproof · cited by 1,504
Cited by1
Results whose statement or proof uses this declaration.
- NormalizedGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 0