Theorems · Theorem · commutative algebra
Ideal.IsPrime.one_notMem
∀ {α : Type u} [inst : Semiring α] {I : Ideal α}, I.IsPrime → 1 ∉ I- Defined in
- Mathlib.RingTheory.Ideal.Prime
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- isUnit_oneproof · cited by 48
- Ideal.notMem_of_isUnitproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.mem_of_pow_memproof · cited by 10
- Ideal.one_notMemproof · cited by 9
- Ideal.IsPrime.notMem_of_isCoprime_of_memproof · cited by 1
- Module.Free.away_of_finite_of_flat_of_rankAtStalk_constantproof · cited by 0