Theorems · Theorem · ring theory
OreLocalization.nontrivial_of_nonZeroDivisorsLeft
∀ {R : Type u_1} [inst : MonoidWithZero R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] [Nontrivial R],
S ≤ nonZeroDivisorsLeft R → Nontrivial (OreLocalization S R)- Cited by
- 1 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.
Cites9
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 and proof · cited by 2,416
- MulZeroClass.zero_mulproof · cited by 1,625
- one_ne_zeroproof · cited by 885
- MonoidWithZerostatement and proof · cited by 456
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- nonZeroDivisorsLeftstatement and proof · cited by 26
- OreLocalization.nontrivial_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.nontrivial_of_nonZeroDivisorsproof · cited by 0