Mathlib Map

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 b

A 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
Assumes
CommSemigroupSMulIsScalarTower

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.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.