Theorems · Theorem · commutative algebra
FractionalIdeal.coeToSubmodule_inj
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- FractionalIdeal.coeToSubmodule_injectiveproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.eq_spanSingleton_of_principalproof · cited by 3
- FractionalIdeal.extended_extendedproof · cited by 1
- FractionalIdeal.extended_coeIdeal_eq_mapproof · cited by 1