Theorems · Theorem · ring theory
Subalgebra.toSubsemiring_injective
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Function.Injective Subalgebra.toSubsemiring- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Subsemiringstatement and proof · cited by 456
- Subalgebra.toSubsemiringstatement and proof · cited by 115
- Subalgebra.extproof · cited by 28
- Subalgebra.mem_toSubsemiringproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- RingCon.liftₐ_rangeproof · cited by 1
- Algebra.toSubsemiring_eq_topproof · cited by 0
- Subalgebra.toSubsemiring_injproof · cited by 0
- Subalgebra.unop_adjoinproof · cited by 0
- Subalgebra.op_adjoinproof · cited by 0