I am studying the QCD chiral symmetry, and by considering the $u$,$d$,$s$ quarks massless, the Lagrangian
\begin{equation} \mathcal{L} = \sum_{i = u,d,s} \bar{q}_{k}i \gamma^{\mu}D_{\mu}q_{k} \end{equation}
where $D_{\mu}$ is the covariant derivativative containing the gluon gauge field, is invariant under $U(3)_{L} \times U(3)_{R}$ and as many textbooks says and also Wikipedia reported is possible to decompose \begin{equation} U(3)_{L} \times U(3)_{R} \quad \mathrm{into} \quad U(1)_{V} \times U(1)_{A} \times SU(3)_{L} \times SU(3)_{R} \end{equation} I am familiar with the relation $$U(N) \simeq SU(N) \times U(1)$$ but I am confused about the $U(1)_{V} \times U(1)_{A}$ product. What tells to the $U(1)$ to be vectorial or axial vectorial? Where the $\gamma_{5}$ of the conserved axial vector current comes from?