Theorems · Theorem · commutative algebra
FractionalIdeal.spanSingleton_one
∀ {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.spanSingleton S 1 = 1- Cited by
- 12 results in Mathlib
- Foundations
- Depth 39 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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- Algebra.smul_defproof · cited by 287
- FractionalIdeal.spanSingletonstatement · cited by 73
- FractionalIdeal.extproof · cited by 13
- FractionalIdeal.mem_one_iffproof · cited by 12
Cited by12
Results whose statement or proof uses this declaration.
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.count_oneproof · cited by 4
- FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealproof · cited by 3
- FractionalIdeal.count_selfproof · cited by 3
- FractionalIdeal.spanSingleton_mul_invproof · cited by 2
- FractionalIdeal.mul_generator_self_invproof · cited by 2
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- FractionalIdeal.one_div_spanSingletonproof · cited by 2
- FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulproof · cited by 1
- FractionalIdeal.count_coeproof · cited by 1
- FractionalIdeal.spanSingleton_div_selfproof · cited by 1
- FractionalIdeal.spanSingleton_powproof · cited by 0