Theorems · Definition · group theory
SemigroupIdeal
(M : Type u_1) → [Mul M] → Type u_1
A (left) semigroup ideal in a semigroup M is a set s such that a * b ∈ s whenever
b ∈ s.
- Defined in
- Mathlib.Algebra.Group.Ideal
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SubMulActionproof · cited by 120
Cited by14
Results whose statement or proof uses this declaration.
- SemigroupIdeal.closurestatement · cited by 11
- SemigroupIdeal.FGstatement and proof · cited by 2
- SemigroupIdeal.coe_closurestatement and proof · cited by 2
- SemigroupIdeal.mem_closure_of_memstatement · cited by 1
- SemigroupIdeal.mul_memstatement and proof · cited by 1
- SemigroupIdeal.closure_lestatement and proof · cited by 1
- SemigroupIdeal.coe_closure'statement · cited by 1
- SemigroupIdeal.mem_closurestatement · cited by 0
- SemigroupIdeal.mem_closure'statement · cited by 0
- SemigroupIdeal.mem_closure''statement · cited by 0
- SemigroupIdeal.subset_closurestatement · cited by 0
- SemigroupIdeal.closure_monostatement · cited by 0