Theorems · Theorem · commutative algebra
FractionalIdeal.spanSingleton_eq_zero_iff
∀ {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] {y : P}, FractionalIdeal.spanSingleton S y = 0 ↔ y = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- Set.mem_singletonproof · cited by 183
- FractionalIdeal.spanSingletonstatement and proof · cited by 73
- FractionalIdeal.coe_spanSingletonproof · cited by 11
- FractionalIdeal.spanSingleton_zeroproof · cited by 11
- FractionalIdeal.coe_zeroproof · cited by 10
- FractionalIdeal.spanSingleton.congr_simpproof · cited by 8
- Submodule.span_eq_botproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.count_well_definedproof · cited by 5
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.spanSingleton_ne_zero_iffproof · cited by 3