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Theorems · Theorem · ring theory

algebraMap.coe_eq_zero_iff

∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [FaithfulSMul R A]
  (a : R), ↑a = 0 ↔ a = 0
Defined in
Mathlib.Algebra.Algebra.Basic
Cited by
1 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraFaithfulSMul
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Around this declaration

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

RCLike.ofReal_eq_zero · cited by 6RCLike.ofReal_eq_zeroSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringFaithfulSMul · cited by 340FaithfulSMulAlgebra.cast · cited by 58Algebra.castFaithfulSMul.algebraMap_eq_zero_iff · cited by 8FaithfulSMul.algebraMap_e…algebraMap.coe_eq_zero_iffCITED BYCITES

Cites6

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Cited by1

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