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 ATurn 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- NonUnitalSubalgebrastatement · cited by 215
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
- Subsemiring.toSubmonoidproof · cited by 153
- Subalgebra.toSubsemiringproof · cited by 115
- Subalgebra.smul_memproof · cited by 20
Cited by12
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.adjoin_le_algebra_adjoinstatement · cited by 1
- Subalgebra.toNonUnitalSubalgebraOrderEmbeddingproof · cited by 1
- Subalgebra.toNonUnitalSubalgebra_injectivestatement · cited by 1
- Subalgebra.toNonUnitalSubalgebra_le_toNonUnitalSubalgebrastatement · cited by 1
- Unitization.lift_rangeproof · cited by 1
- Unitization.lift_range_lestatement and proof · cited by 1
- Subalgebra.mem_toNonUnitalSubalgebrastatement · cited by 0
- Subalgebra.one_mem_toNonUnitalSubalgebrastatement · cited by 0
- NonUnitalSubalgebra.toSubalgebra_toNonUnitalSubalgebrastatement and proof · cited by 0
- Subalgebra.toNonUnitalSubalgebra_injstatement · cited by 0
- Subalgebra.toNonUnitalSubalgebra_monostatement · cited by 0
- Subalgebra.toNonUnitalSubalgebra_toSubalgebrastatement and proof · cited by 0