ON THE GOLDIE-DIMENSION OF INJECTIVE-MODULES

Let M be an essentially finitely generated injective (or, more general ly, quasi-continuous) module. It is shown that if M satisfies a mild u niqueness condition on essential closures of certain submodules, then the existence of an infinite independent set of submodules of M implie s the existence of a larger independent set on some quotient of M modu le a directed union of direct summands. This provides new characterisa tions of injective (or quasi-continuous) modules of finite Goldie dime nsion. These results are then applied to the study of indecomposable d ecompositions of quasi-continuous modules and nonsingular CS modules.