Theorems · Theorem · commutative algebra
IsSMulRegular.mul_iff
∀ {R : Type u_1} {M : Type u_3} {a b : R} [inst : CommSemigroup R] [inst_1 : SMul R M] [IsScalarTower R R M],
IsSMulRegular M (a * b) ↔ IsSMulRegular M a ∧ IsSMulRegular M bA product is M-regular if and only if the factors are.
- Defined in
- Mathlib.Algebra.Regular.SMul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsScalarTowerstatement and proof · cited by 3,896
- mul_commproof · cited by 2,262
- IsSMulRegularstatement and proof · cited by 128
- CommSemigroupstatement and proof · cited by 62
- IsSMulRegular.mul_and_mul_iffproof · cited by 1
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