The formula dim(A+B)=dim(A)+dim(B)-dim(A and B) works when 'dim' stand
s for the dimension of subspaces A,B f any vector space. In general, h
owever, it does no longer hold if 'dim' means the uniform (or Goldie)
dimension of submodules A,B of a module M over a ring R, and in fact t
he left hand side may be infinite while the right had side is finite.
In this paper we shall give a characterization of those modules M in w
hich the formula holds for any two submodules A,B, as well as some con
ditions In the ring R which guarantee that dim(A+B) is finite whenever
A and B are finite dimensional R-modules.