In this paper the structure of
finitely generated splitting rings for the Goldie theory is studied. First, right
nonsingular finitely generated splitting rings with essential socle which either are
right finite dimensional or are right orders in a semiprimary ring are characterized.
This characterization is in terms of an explicit triangular matrix structure
for R. Then right nonsingular finitely generated splitting rings with zero
socle are shown to be right finite dimensional if and only if they are right
orders in a semiprimary ring. An explicit triangular structure is given for this
class of rings as well. For certain classes of right nonsingular right finite
dimensional finitely generated splitting rings with zero socle, the structure
theorem can be simplified somewhat. Then right nonsingular right finite
dimensional finitely generated splitting rings are characterized as a certain
essential product of a ring with essential socle and one with zero socle. Right
nonsingular finitely generated splitting rings which are right orders in a
semiprimary ring are shown to be a direct product of a ring with essential socle
and a ring with zero socle. Finally, some comments are made showing how
some of these results can be applied to bounded splitting rings and splitting
rings.
