Theorems · Theorem · commutative algebra
FractionalIdeal.coeIdeal_span_singleton
∀ {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 : R), ↑(Ideal.span {x}) = FractionalIdeal.spanSingleton S ((algebraMap R P) x)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- map_mulproof · cited by 1,137
- Ideal.spanstatement and proof · cited by 948
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- smul_eq_mulproof · cited by 357
Cited by10
Results whose statement or proof uses this declaration.
- FractionalIdeal.count_well_definedproof · cited by 5
- FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealproof · cited by 3
- FractionalIdeal.finprod_heightOneSpectrum_factorizationproof · cited by 2
- NumberField.exists_ideal_in_class_of_norm_leproof · cited by 1
- conductor_mul_differentIdealproof · cited by 1
- FractionalIdeal.coe_ideal_span_singleton_mul_invproof · cited by 1
- IsDedekindDomain.exists_add_spanSingleton_mul_eqproof · cited by 1
- FractionalIdeal.sup_mul_infproof · cited by 0
- FractionalIdeal.coe_ideal_span_singleton_div_selfproof · cited by 0