Theorems · Theorem · ring theory
OreLocalization.nontrivial_of_nonZeroDivisorsRight
∀ {R : Type u_1} [inst : MonoidWithZero R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] [Nontrivial R],
S ≤ nonZeroDivisorsRight R → Nontrivial (OreLocalization S R)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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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.mul_zeroproof · cited by 2,091
- one_ne_zeroproof · cited by 885
- MonoidWithZerostatement and proof · cited by 456
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- nonZeroDivisorsRightstatement and proof · cited by 26
- OreLocalization.nontrivial_iffproof · cited by 2
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