Theorems · Theorem · ring theory
OreLocalization.nontrivial_iff
∀ {R : Type u_1} [inst : MonoidWithZero R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S],
Nontrivial (OreLocalization S R) ↔ 0 ∉ S- Defined in
- Mathlib.RingTheory.OreLocalization.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- Nontrivialstatement · cited by 2,416
- MonoidWithZerostatement and proof · cited by 456
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- not_subsingleton_iff_nontrivialproof · cited by 21
- OreLocalization.subsingleton_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- OreLocalization.nontrivial_of_nonZeroDivisorsLeftproof · cited by 1
- OreLocalization.nontrivial_of_nonZeroDivisorsRightproof · cited by 0