Theorems · Theorem · commutative algebra
FractionalIdeal.spanSingleton_zero
∀ {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 0 = 0- Cited by
- 11 results in Mathlib
- Foundations
- Depth 40 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
- smul_zeroproof · cited by 665
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- FractionalIdeal.spanSingletonstatement · cited by 73
- FractionalIdeal.extproof · cited by 13
Cited by11
Results whose statement or proof uses this declaration.
- ClassGroup.mk_eq_one_iffproof · cited by 4
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.constant_factor_ne_zeroproof · cited by 3
- FractionalIdeal.spanSingleton_eq_zero_iffproof · cited by 3
- FractionalIdeal.mul_generator_self_invproof · cited by 2
- FractionalIdeal.one_div_spanSingletonproof · cited by 2
- FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulproof · cited by 1
- ClassGroup.mk0_eq_mk0_iff_exists_fraction_ringproof · cited by 1
- FractionalIdeal.finprod_heightOneSpectrum_factorization_principalproof · cited by 0
- mem_principal_ideals_iffproof · cited by 0
- FractionalIdeal.invertible_iff_generator_nonzeroproof · cited by 0