Theorems · Theorem · commutative algebra
FractionalIdeal.zero_of_num_eq_bot
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
[IsDomain R] [Module.IsTorsionFree R P], 0 ∉ S → ∀ {I : FractionalIdeal S P}, I.num = ⊥ → I = 0- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Submonoidstatement and proof · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- Submodule.mapproof · cited by 614
- Module.IsTorsionFreestatement and proof · cited by 600
- FractionalIdealstatement and proof · cited by 423
- eq_bot_iffproof · cited by 159
- Algebra.linearMapproof · cited by 157
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.num_eq_zero_iffproof · cited by 3
- FractionalIdeal.absNorm_eq_zero_iffproof · cited by 0