Theorems · Theorem · commutative algebra
FractionalIdeal.canonicalEquiv_self
∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) (P : Type u_2) [inst_1 : CommRing P] [inst_2 : Algebra R P]
[inst_3 : IsLocalization S P], FractionalIdeal.canonicalEquiv S P P = RingEquiv.refl (FractionalIdeal S P)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Algebrastatement and proof · cited by 11,388
- Submonoidstatement and proof · cited by 3,086
- RingEquivstatement and proof · cited by 1,147
- IsLocalizationstatement and proof · cited by 636
- RingEquiv.symmproof · cited by 567
- FractionalIdealstatement and proof · cited by 423
- RingEquiv.reflstatement and proof · cited by 72
- RingEquiv.transproof · cited by 54
- FractionalIdeal.canonicalEquivstatement and proof · cited by 19
- FractionalIdeal.canonicalEquiv_symmproof · cited by 2
- FractionalIdeal.canonicalEquiv_trans_canonicalEquivproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ClassGroup.mk_eq_one_iffproof · cited by 4
- ClassGroup.Quot_mk_eq_mkproof · cited by 3
- ClassGroup.mk_eq_mkproof · cited by 2
- ClassGroup.inductionproof · cited by 1