Theorems · Theorem · commutative algebra
FractionalIdeal.mem_spanSingleton_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] (x : P), x ∈ FractionalIdeal.spanSingleton S x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- one_smulproof · cited by 1,374
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- FractionalIdeal.spanSingletonstatement · cited by 73
- FractionalIdeal.mem_spanSingletonproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_topproof · cited by 1
- FractionalIdeal.extended_spanSingletonproof · cited by 1
- FractionalIdeal.invertible_iff_generator_nonzeroproof · cited by 0