G. J. Janusz defined a splitting
ring R for a group G of order n invertible in R. Then, the Brauer splitting theorem
was given by G. Szeto which proves the existence of a finitely generated projective
and separable splitting ring for G. Let M be a RG-module and R0 be a
subring of R. Then we say that M is realizable in R0 if and only if there
exists a R0G-module N such that M≅R ⊗R0N as left RG-modules. This
paper gives a characterization of splitting rings in terms of the concept of
realizability as in the field case. The other main results in this paper are the
structure theorem for split group algebras and some properties of group
characters.
