Theorems · Theorem · commutative algebra
FractionalIdeal.ext
∀ {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}, (∀ (x : P), x ∈ I ↔ x ∈ J) → I = J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- SetLike.extproof · cited by 92
Cited by13
Results whose statement or proof uses this declaration.
- FractionalIdeal.spanSingleton_oneproof · cited by 12
- FractionalIdeal.spanSingleton_zeroproof · cited by 11
- FractionalIdeal.coeIdeal_span_singletonproof · cited by 10
- FractionalIdeal.exists_eq_spanSingleton_mulproof · cited by 6
- FractionalIdeal.le_one_iff_exists_coeIdealproof · cited by 5
- FractionalIdeal.canonicalEquiv_canonicalEquivproof · cited by 3
- FractionalIdeal.map_coeIdealproof · cited by 2
- FractionalIdeal.canonicalEquiv_coeIdealproof · cited by 2
- FractionalIdeal.extended_spanSingletonproof · cited by 1
- FractionalIdeal.map_injectiveproof · cited by 0
- FractionalIdeal.ringEquivOfRingEquiv_reflproof · cited by 0
- FractionalIdeal.div_oneproof · cited by 0