In the book Quantum Mechanics - Franz Schwabl, in chapter 10, equation (10.4) says
Since all the properties of angular momenta and their eigenstates hold for the total angular momentum J .We can construct the product states: $$|j_1m_1j_2m_2\rangle=|j_1m_1\rangle|j_2m_2\rangle$$
I want to know why multiplication? instead of other relations like: $$|j_1m_1j_2m_2\rangle=|j_1m_1\rangle+|j_2m_2\rangle$$
or some weird relations?
Any help will be greatly appreciated!