Theorems · Theorem · ring theory
NoZeroDivisors.of_faithfulSMul
∀ (R : Type u_1) (A : Type u_3) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [FaithfulSMul R A] [NoZeroDivisors A], NoZeroDivisors R
- Defined in
- Mathlib.Algebra.Algebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- map_zeroproof · cited by 1,614
- map_mulproof · cited by 1,137
- NoZeroDivisorsstatement and proof · cited by 545
- FaithfulSMulstatement and proof · cited by 340
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- Function.Injective.noZeroDivisorsproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgebraic.restrictScalarsproof · cited by 6