Theorems · Theorem · commutative algebra
IsArtinianRing.nonZeroDivisorsLeft_eq_isUnitSubmonoid
∀ (R : Type u_1) [inst : Ring R] [IsArtinianRing Rᵐᵒᵖ], IsUnit.submonoid R = nonZeroDivisorsLeft R
- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIsArtinianRing
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.
- Ringstatement and proof · cited by 7,463
- Submonoidstatement · cited by 3,086
- MulOppositestatement and proof · cited by 1,135
- IsArtinianRingstatement and proof · cited by 98
- IsUnit.submonoidstatement and proof · cited by 56
- Submonoid.extproof · cited by 48
- nonZeroDivisorsLeftstatement · cited by 26
- isLeftRegular_iff_mem_nonZeroDivisorsLeftproof · cited by 3
- IsArtinianRing.isUnit_iff_isLeftRegularproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.