Theorems · Theorem · ring theory
Subalgebra.coe_eq_zero
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A)
{x : ↥S}, ↑x = 0 ↔ x = 0- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- ZeroMemClass.coe_eq_zeroproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.one_le_of_lt_oneproof · cited by 2
- MvPolynomial.esymmAlgHom_fin_injectiveproof · cited by 2
- Subalgebra.inv_mem_of_algebraicproof · cited by 1
- Subalgebra.isField_of_algebraicproof · cited by 0