Theorems · Theorem · commutative algebra
IsBezout.TFAE
∀ {R : Type u} [inst : CommRing R] [IsBezout R] [IsDomain R],
[IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE- Defined in
- Mathlib.RingTheory.Bezout
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Submoduleproof · cited by 7,192
- Idealproof · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Ideal.spanproof · cited by 948
- UniqueFactorizationMonoidstatement and proof · cited by 279
- IsNoetherianRingstatement and proof · cited by 268
- Submodule.FGproof · cited by 230
- IsPrincipalIdealRingstatement and proof · cited by 131
- List.TFAEstatement · cited by 102
- Ideal.FGproof · cited by 99
- List.tfae_of_cycleproof · cited by 83
Cited by2
Results whose statement or proof uses this declaration.
- tfae_of_isNoetherianRing_of_isLocalRing_of_isDomainproof · cited by 1
- Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrderedproof · cited by 1