Theorems · Theorem · ring theory
isRightRegular_iff_mem_nonZeroDivisorsRight
∀ {R : Type u_1} [inst : Ring R] {r : R}, IsRightRegular r ↔ r ∈ nonZeroDivisorsRight R- Defined in
- Mathlib.Algebra.Ring.NonZeroDivisors
- Cited by
- 2 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
- IsRightRegularstatement · cited by 93
- nonZeroDivisorsRightstatement · cited by 26
- isRightRegular_iff_left_eq_zero_of_mulproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- mul_cancel_right_mem_nonZeroDivisorsRightproof · cited by 1
- IsArtinianRing.isUnitSubmonoid_eq_nonZeroDivisorsRightproof · cited by 0