Theorems · Theorem · order theory
SemigroupIdeal.fg_of_wellQuasiOrderedLE
∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : PartialOrder M] [WellQuasiOrderedLE M] [CanonicallyOrderedMul M]
(I : SemigroupIdeal M), I.FGIn a canonically ordered and well-quasi-ordered monoid, any semigroup ideal is finitely generated.
- Defined in
- Mathlib.Algebra.Order.Group.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- CommMonoidstatement and proof · cited by 2,264
- Minimalproof · cited by 150
- Set.IsPWOproof · cited by 99
- CanonicallyOrderedMulstatement and proof · cited by 51
- WellQuasiOrderedLEstatement and proof · cited by 22
- SemigroupIdealstatement and proof · cited by 12
- Set.IsPWO.monoproof · cited by 11
- SemigroupIdeal.closureproof · cited by 11
- IsAntichain.finite_of_partiallyWellOrderedOnproof · cited by 6
- SubMulAction.smul_memproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.