Theorems · Theorem · ring theory
isLeftRegular_iff_mem_nonZeroDivisorsLeft
∀ {R : Type u_1} [inst : Ring R] {r : R}, IsLeftRegular r ↔ r ∈ nonZeroDivisorsLeft R- Defined in
- Mathlib.Algebra.Ring.NonZeroDivisors
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsLeftRegularstatement · cited by 97
- nonZeroDivisorsLeftstatement · cited by 26
- isLeftRegular_iff_right_eq_zero_of_mulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- dvd_cancel_left_mem_nonZeroDivisorsproof · cited by 3
- mul_cancel_left_mem_nonZeroDivisorsLeftproof · cited by 1
- IsArtinianRing.nonZeroDivisorsLeft_eq_isUnitSubmonoidproof · cited by 0