  In this short note we want to give a definition of a generalized Deligne
pairing for modules over an Azumaya algebra on an arithmetic surface $X$. We do
this by defining Hermitian metrics on the Azumaya algebra and on the modules in
question. Then we go on and define the determinant of the cohomology for a pair
of modules over an Azumaya algebra. Using this we give the definition of a
generalized Deligne pairing and study some of its properties.
