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Theorems · Definition · ring theory

Subalgebra.toNonUnitalSubalgebra

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → Subalgebra R A → NonUnitalSubalgebra R A

Turn a Subalgebra into a NonUnitalSubalgebra by forgetting that it contains 1.

Defined in
Mathlib.Algebra.Algebra.Subalgebra.Basic
Cited by
11 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebra

Around this declaration

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

NonUnitalAlgebra.adjoin_le_algebra_adjoin · cited by 1NonUnitalAlgebra.adjoin_l…Subalgebra.toNonUnitalSubalgebraOrderEmbedding · cited by 1Subalgebra.toNonUnitalSub…Subalgebra.toNonUnitalSubalgebra_injective · cited by 1Subalgebra.toNonUnitalSub…Subalgebra.toNonUnitalSubalgebra_le_toNonUnitalSubalgebra · cited by 1Subalgebra.toNonUnitalSub…Unitization.lift_range · cited by 1Unitization.lift_rangeUnitization.lift_range_le · cited by 1Unitization.lift_range_leSubalgebra.mem_toNonUnitalSubalgebra · cited by 0Subalgebra.mem_toNonUnita…Subalgebra.one_mem_toNonUnitalSubalgebra · cited by 0Subalgebra.one_mem_toNonU…NonUnitalSubalgebra.toSubalgebra_toNonUnitalSubalgebra · cited by 0NonUnitalSubalgebra.toSub…Subalgebra.toNonUnitalSubalgebra_inj · cited by 0Subalgebra.toNonUnitalSub…Subalgebra.toNonUnitalSubalgebra_mono · cited by 0Subalgebra.toNonUnitalSub…Subalgebra.toNonUnitalSubalgebra_toSubalgebra · cited by 0Subalgebra.toNonUnitalSub…Semiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringSubalgebra · cited by 1353SubalgebraNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraSubsemigroup.carrier · cited by 160Subsemigroup.carrierSubmonoid.toSubsemigroup · cited by 159Submonoid.toSubsemigroupSubsemiring.toSubmonoid · cited by 153Subsemiring.toSubmonoidSubalgebra.toSubsemiring · cited by 115Subalgebra.toSubsemiringSubalgebra.smul_mem · cited by 20Subalgebra.smul_memSubalgebra.toNonUnitalSubalge…CITED BYCITES

Cites10

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

Cited by12

Results whose statement or proof uses this declaration.