Theorems · Theorem · commutative algebra
FractionalIdeal.coe_le_coe
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
{I J : FractionalIdeal S P}, ↑I ≤ ↑J ↔ I ≤ J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmodulestatement · cited by 130
Cited by10
Results whose statement or proof uses this declaration.
- FractionalIdeal.le_div_iff_mul_leproof · cited by 3
- FractionalIdeal.spanSingleton_le_iff_memproof · cited by 3
- FractionalIdeal.le_dual_iffproof · cited by 2
- FractionalIdeal.one_leproof · cited by 2
- differentialIdeal_le_fractionalIdeal_iffproof · cited by 1
- FractionalIdeal.dual_eq_dual_mul_dualproof · cited by 1
- FractionalIdeal.mul_one_div_le_oneproof · cited by 1
- FractionalIdeal.le_self_mul_one_divproof · cited by 1
- IsDedekindDomain.differentIdeal_dvd_map_differentIdealproof · cited by 1
- Submodule.traceDual_eq_span_map_traceDual_of_linearDisjointproof · cited by 0