  In this paper, we discuss the inverse problem of determining a semisimple
group algebra from the knowledge of rings of the type sum_{t=1}^s M_{n_t}(Ft),
where j is an arbitrary integer and F_t is finite field for each t, and show
that it is ill-posed. After then, we define the concept of completeness of the
rings of the type sum_{t=1}^s M_{n_t}(Ft) to pose a well-posed inverse problem
and propose a conjecture in this direction.
