Decomposability of finitely presented modules

It is proved that a commutative ring with 1 has the property that every finitely presented module is a summand of a direct sum of cyclic modules if and only if it is locally a gen- eralized valuation ring. A Noetherian ring has this property if and only if it is a direct product of a finite number of Dedekind do- mains and an Artinian principal ideal ring. Any commutative local ring which is not a generalized valuation ring has finitely presented indecomposable modules requiring arbitrarily large