Theorems · Theorem · commutative algebra
Ideal.dvdNotUnit_iff_lt
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {I J : Ideal A}, DvdNotUnit I J ↔ J < I- Cited by
- 3 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- IsUnitproof · cited by 1,602
- le_of_ltproof · cited by 1,175
- IsDedekindDomainstatement and proof · cited by 668
- lt_of_le_of_neproof · cited by 230
- not_le_of_gtproof · cited by 97
- isUnit_oneproof · cited by 48
- mul_left_cancel₀proof · cited by 47
- DvdNotUnitstatement and proof · cited by 33
- Ideal.dvd_iff_leproof · cited by 33
Cited by3
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizerproof · cited by 3
- Ideal.pow_right_strictAntiproof · cited by 2
- Ideal.eq_prime_pow_of_succ_lt_of_leproof · cited by 1