Theorems · Theorem · commutative algebra
IsBezout.isPrincipal_of_FG
∀ {R : Type u} {inst : Semiring R} [self : IsBezout R] (I : Ideal R), I.FG → Submodule.IsPrincipal IAny finitely generated ideal is principal.
- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsBezout
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- Submodule.IsPrincipalstatement · cited by 129
- Ideal.FGstatement · cited by 99
- IsBezoutstatement and proof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Module.Flat.flat_iff_torsion_eq_bot_of_isBezoutproof · cited by 1
- Polynomial.isPrimitive_iff_contentIdeal_eq_topproof · cited by 1