Theorems · Theorem · commutative algebra
FractionalIdeal.isFractional_of_fg
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
[IsLocalization S P] {I : Submodule R P}, I.FG → IsFractional S I- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 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.
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- Submodule.spanproof · cited by 1,504
- IsLocalizationstatement and proof · cited by 636
- Submodule.FGstatement and proof · cited by 230
- IsLocalization.IsIntegerproof · cited by 39
- IsFractionalstatement · cited by 29
- FractionalIdeal.isFractional_span_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Units.submodule_isFractionalproof · cited by 1
- FractionalIdeal.isFractional_adjoin_integralproof · cited by 0