Theorems · Definition · ring theory
Subsemigroup.nonUnitalSubsemiringClosure
{R : Type u} → [inst : NonUnitalNonAssocSemiring R] → Subsemigroup R → NonUnitalSubsemiring RThe additive closure of a non-unital subsemigroup is a non-unital subsemiring.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- AddSubmonoidproof · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Subsemigroupstatement and proof · cited by 323
- AddSubmonoid.closureproof · cited by 224
- NonUnitalSubsemiringstatement · cited by 201
Cited by4
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.sumSqproof · cited by 6
- Subsemigroup.nonUnitalSubsemiringClosure_eq_closurestatement and proof · cited by 2
- Subsemigroup.nonUnitalSubsemiringClosure_toAddSubmonoidstatement · cited by 0
- Subsemigroup.nonUnitalSubsemiringClosure_coestatement · cited by 0