Theorems · Theorem · commutative algebra
FractionalIdeal.coeIdeal_le_coeIdeal
∀ {R : Type u_1} [inst : CommRing R] (K : Type u_3) [inst_1 : CommRing K] [inst_2 : Algebra R K] [IsFractionRing R K]
{I J : Ideal R}, ↑I ≤ ↑J ↔ I ≤ J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Idealstatement and proof · cited by 4,748
- nonZeroDivisorsstatement · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coeIdealstatement · cited by 109
- IsFractionRing.coeSubmodule_le_coeSubmoduleproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- differentialIdeal_le_iffproof · cited by 2
- Ideal.exist_integer_multiples_notMemproof · cited by 1
- IsDedekindDomain.differentIdeal_dvd_map_differentIdealproof · cited by 1
- IsDedekindDomain.exists_add_spanSingleton_mul_eqproof · cited by 1
- FractionalIdeal.mul_inv_cancel_of_le_oneproof · cited by 1
- Submodule.traceDual_eq_span_map_traceDual_of_linearDisjointproof · cited by 0