Theorems · Theorem · commutative algebra
IsFractionRing.coeSubmodule_le_coeSubmodule
∀ {R : Type u_3} {K : Type u_4} [inst : CommRing R] [inst_1 : CommRing K] [inst_2 : Algebra R K] [IsFractionRing R K]
{I J : Ideal R}, IsLocalization.coeSubmodule K I ≤ IsLocalization.coeSubmodule K J ↔ I ≤ J- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, 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
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- le_rflproof · cited by 1,558
- IsFractionRingstatement and proof · cited by 738
- IsLocalization.coeSubmodulestatement · cited by 30
- IsLocalization.coeSubmodule_le_coeSubmoduleproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.coeIdeal_le_coeIdealproof · cited by 6
- IsFractionRing.coeSubmodule_injectiveproof · cited by 0
- IsFractionRing.coeSubmodule_strictMonoproof · cited by 0