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Theorems · Definition · group theory

SemigroupIdeal.FG

{M : Type u_1} → [inst : Mul M] → SemigroupIdeal M → Prop

A semigroup ideal is finitely generated if it is generated by a finite set. This is defeq to SubMulAction.FG, but unfolds more nicely.

Defined in
Mathlib.Algebra.Group.Ideal
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
Mul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SemigroupIdeal.fg_iff · cited by 0SemigroupIdeal.fg_iffSemigroupIdeal.fg_of_wellQuasiOrderedLE · cited by 0SemigroupIdeal.fg_of_well…Set · cited by 53352SetSet.Finite · cited by 1814Set.FiniteSemigroupIdeal · cited by 12SemigroupIdealSemigroupIdeal.closure · cited by 11SemigroupIdeal.closureSemigroupIdeal.FGCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.