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Theorems · Definition · ring theory

NonUnitalSubsemiring.toSubsemigroup

{R : Type u} → [inst : NonUnitalNonAssocSemiring R] → NonUnitalSubsemiring R → Subsemigroup R

Reinterpret a NonUnitalSubsemiring as a Subsemigroup.

Defined in
Mathlib.RingTheory.NonUnitalSubsemiring.Defs
Cited by
12 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
NonUnitalNonAssocSemiring
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Around this declaration

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

NonUnitalSubsemiring.map · cited by 22NonUnitalSubsemiring.mapNonUnitalSubsemiring.comap · cited by 14NonUnitalSubsemiring.comapNonUnitalSubsemiring.prod · cited by 9NonUnitalSubsemiring.prodNonUnitalSubring.toSubsemigroup · cited by 8NonUnitalSubring.toSubsem…NonUnitalSubsemiring.topologicalClosure · cited by 5NonUnitalSubsemiring.topo…NonUnitalSubsemiring.copy · cited by 4NonUnitalSubsemiring.copyRingEquiv.nonUnitalSubsemiringMap · cited by 2RingEquiv.nonUnitalSubsem…NonUnitalSubsemiring.mem_iSup_of_directed · cited by 2NonUnitalSubsemiring.mem_…NonUnitalSubsemiring.toSubsemigroup_strictMono · cited by 1NonUnitalSubsemiring.toSu…NonUnitalSubsemiring.closure_subsemigroup_closure · cited by 1NonUnitalSubsemiring.clos…NonUnitalSubsemiring.mk'_toSubsemigroup · cited by 1NonUnitalSubsemiring.mk'_…NonUnitalStarSubalgebra.nonUnitalCommRingTopologicalClosure · cited by 1NonUnitalStarSubalgebra.n…NonUnitalSubsemiring.centralizer_toSubsemigroup · cited by 0NonUnitalSubsemiring.cent…NonUnitalSubsemiring.sInf_toSubsemigroup · cited by 0NonUnitalSubsemiring.sInf…NonUnitalSubsemiring.closure_addSubmonoid_closure · cited by 0NonUnitalSubsemiring.clos…NonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringSubsemigroup · cited by 323SubsemigroupNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringAddSubmonoid.toAddSubsemigroup · cited by 198AddSubmonoid.toAddSubsemi…AddSubsemigroup.carrier · cited by 198AddSubsemigroup.carrierNonUnitalSubsemiring.toAddSubmonoid · cited by 56NonUnitalSubsemiring.toAd…NonUnitalSubsemiring.mul_mem' · cited by 2NonUnitalSubsemiring.mul_…NonUnitalSubsemiring.toSubsem…CITED BYCITES

Cites7

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

Cited by22

Results whose statement or proof uses this declaration.