A splitting ring of global dimension two

In this paper an example is given of a ring with left global dimension 2 having the property that the singular submodule of any R-module A is a direct summand of A. Although the example given is quite specific, the methods can be used to construct a fairly large class of these rings. In this paper, all rings are assumed to be associative with an identity element, and all modules will be unitary left modules. An R-module A is said to split if the singular submodule, Z(RA), is a direct summand of A. R is called a splitting ring if every R-module splits (see [1], [3], and [7]). In [3] Cateforis and Sandomierski have shown that every commutative splitting ring has left global dimension _1. M. L. Teply [7] has shown that if the commutative hypothesis is dropped, then every splitting ring must have left global dimension