  It is proved that the unital Banach algebra of almost periodic functions of
several variables with Bohr-Fourier spectrum in a given additive semigroup is
an Hermite ring. The same property holds for the Wiener algebra of functions
that in addition have absolutely convergent Bohr-Fourier series. As
applications of the Hermite property of these algebras, we study factorizations
of Wiener--Hopf type of rectangular matrix functions and the Toeplitz corona
problem in the context of almost periodic functions of several variables.
