Theorems · Theorem · commutative algebra
isRegular_mul_iff
∀ {R : Type u_1} [inst : CommSemigroup R] {a b : R}, IsRegular (a * b) ↔ IsRegular a ∧ IsRegular bA product is regular if and only if the factors are.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- IsRegularstatement and proof · cited by 116
- CommSemigroupstatement and proof · cited by 62
- isRegular_mul_and_mul_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsRegular.of_mul_leftproof · cited by 2
- IsRegular.of_mul_rightproof · cited by 0