English
The map algebraMap₀ is multiplicative: algebraMap₀(r s) equals algebraMap₀(r) algebraMap₀(s) inside the tensor power.
Русский
Отображение algebraMap₀ сохраняет умножение: algebraMap₀(rs) равно algebraMap₀(r) algebraMap₀(s) внутри тензорного произведения.
LaTeX
$$$ \\operatorname{algebraMap}_0(r s) = \\operatorname{algebraMap}_0(r) \\operatorname{algebraMap}_0(s) $$$
Lean4
theorem algebraMap₀_mul_algebraMap₀ (r s : R) :
cast R M (add_zero _) (algebraMap₀ r ₜ* algebraMap₀ s) = algebraMap₀ (r * s) :=
by
rw [← smul_eq_mul, LinearEquiv.map_smul]
exact algebraMap₀_mul r (@algebraMap₀ R M _ _ _ s)