Theorems · Theorem · commutative algebra
Ideal.one_notMem
∀ {α : Type u} [inst : Semiring α] (I : Ideal α) [hI : I.IsPrime], 1 ∉ I- Defined in
- Mathlib.RingTheory.Ideal.Prime
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringIdeal.IsPrime
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.IsPrime.one_notMemproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.primeComplproof · cited by 462
- Ideal.disjoint_primeCompl_of_liesOverproof · cited by 3
- ValuationSubring.ofPrime_idealOfLEproof · cited by 2
- Module.notMem_support_iff'proof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_auxproof · cited by 1
- Ideal.isPrime_nat_iffproof · cited by 1
- Ideal.le_ker_atPrime_of_forall_exists_eq_mulproof · cited by 1
- Module.isLocallyConstant_rankAtStalk_freeLocusproof · cited by 1
- not_dvd_differentIdeal_iffproof · cited by 1