Theorems · Inductive type · commutative algebra
IsRegular
{R : Type u_1} → [Mul R] → R → PropA regular element is an element c such that multiplication by c both on the left and
on the right is injective.
- Defined in
- Mathlib.Algebra.Regular.Defs
- Cited by
- 116 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by123
Results whose statement or proof uses this declaration.
- IsRegular.leftstatement and proof · cited by 39
- IsRegular.rightstatement and proof · cited by 19
- IsRegular.of_ne_zerostatement · cited by 15
- IsUnit.isRegularstatement · cited by 10
- isRegular_onestatement · cited by 8
- IsRegular.ne_zerostatement and proof · cited by 7
- IsRegular.isSMulRegularstatement · cited by 6
- isRegular_iffstatement and proof · cited by 6
- isRegular_iff_mem_nonZeroDivisorsstatement · cited by 6
- Module.IsTorsionFree.trans_faithfulSMulproof · cited by 6
- Commute.isRegular_iffstatement and proof · cited by 5
- IsRegular.starstatement and proof · cited by 5