ON INDECOMPOSABLE DECOMPOSITIONS OF CS-MODULES

It is shown that, over any ring R, the direct sum M = (+i is an elemen t of l)M(i) of uniform right R-modules M(i) with local endomorphism ri ngs is a CS-module if and only if every uniform submodule of M is esse ntial in a direct summand of M and there does not exist an infinite se quence of non-isomorphic monomorphisms [GRAPHICS] with distinct i(n) i s an element of I. As a consequence, any CS-module which is a direct s um of submodules with local endomorphism rings has the exchange proper ty.