Theorems · Theorem · ring theory
isDomain_iff_cancelMulZero_and_nontrivial
∀ (α : Type u_3) [inst : Semiring α], IsDomain α ↔ IsCancelMulZero α ∧ Nontrivial α
- Defined in
- Mathlib.Algebra.Ring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- IsCancelMulZerostatement and proof · cited by 177
Cited by1
Results whose statement or proof uses this declaration.
- isDomain_iff_noZeroDivisors_and_nontrivialproof · cited by 7