Theorems · Theorem · commutative algebra
FractionalIdeal.exists_notMem_one_of_ne_bot
∀ {A : Type u_2} {K : Type u_3} [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K]
[inst_3 : IsFractionRing A K] [inst_4 : IsDedekindDomain A] {I : Ideal A}, I ≠ ⊥ → I ≠ ⊤ → ∃ x ∈ (↑I)⁻¹, x ∉ 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- nonZeroDivisorsstatement · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coeIdealstatement · cited by 109
- Set.not_subsetproof · cited by 31
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