FormalConjectures.Mathoverflow.«507128»

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import FormalConjecturesUtil

Mathoverflow 507128

Reference: mathoverflow/507128 asked by user Junyan Xu


namespace Mathoverflow507128

There exists a proper ideal I in a (commutative) total ring R of fractions that is an invertible module. If I ⊊ R is such an example, I must have infinite order in the Picard group, and R must not be Noetherian (otherwise it must be semi-local and therefore have trivial Picard group).

@[category research open, AMS 13]
theorem declaration uses 'sorry'exists_isFractionRing_self_ideal_ne_top_invertible :
    ∃ (R : Type) (_ : CommRing R) (_ : IsFractionRing R R) (I : Ideal R),
      I ≠ ⊤ ∧ Module.Invertible R I := by⊢ ∃ R x, ∃ (_ : IsFractionRing R R), ∃ I, I ≠ ⊤ ∧ Module.Invertible R ↥I
  sorryAll goals completed! 🐙


end Mathoverflow507128