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Theorems · Definition · commutative algebra

Subsemiring.toNonUnitalSubsemiring

{R : Type u} → [inst : NonAssocSemiring R] → Subsemiring R → NonUnitalSubsemiring R

Turn a Subsemiring into a NonUnitalSubsemiring by forgetting that it contains 1.

Defined in
Mathlib.Algebra.Ring.Subsemiring.Defs
Cited by
10 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
NonAssocSemiring
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Around this declaration

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

Subsemiring.toNonUnitalSubsemiring_injective · cited by 2Subsemiring.toNonUnitalSu…Submonoid.subsemiringClosure_toNonUnitalSubsemiring · cited by 1Submonoid.subsemiringClos…Subsemiring.sumSq_toNonUnitalSubsemiring · cited by 0Subsemiring.sumSq_toNonUn…Subsemiring.mem_toNonUnitalSubsemiring · cited by 0Subsemiring.mem_toNonUnit…Subsemiring.toNonUnitalSubsemiring_inj · cited by 0Subsemiring.toNonUnitalSu…Subsemiring.toNonUnitalSubsemiring_toSubsemiring · cited by 0Subsemiring.toNonUnitalSu…Subsemiring.closure_isSquare · cited by 0Subsemiring.closure_isSqu…Subsemiring.coe_toNonUnitalSubsemiring · cited by 0Subsemiring.coe_toNonUnit…NonUnitalSubsemiring.toSubsemiring_toNonUnitalSubsemiring · cited by 0NonUnitalSubsemiring.toSu…Subsemiring.one_mem_toNonUnitalSubsemiring · cited by 0Subsemiring.one_mem_toNon…NonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringSubsemigroup.carrier · cited by 160Subsemigroup.carrierSubmonoid.toSubsemigroup · cited by 159Submonoid.toSubsemigroupSubsemiring.toSubmonoid · cited by 153Subsemiring.toSubmonoidSubsemiring.add_mem' · cited by 0Subsemiring.add_mem'Subsemiring.zero_mem' · cited by 0Subsemiring.zero_mem'Subsemiring.toNonUnitalSubsem…CITED BYCITES

Cites8

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

Cited by10

Results whose statement or proof uses this declaration.