On the Decomposition of Continuous Modules

Abstract We prove two theorems on continuous modules: Decomposition Theorem. A continuous module M has a decomposition, M = M 1 ⊕ M 2, such that M 1 is essential over a direct sum of indecomposable summands A i of M, and M 2 has no uniform submodules; and these data are uniquely determined by M up to isomorphism. Direct Sum Theorem. A finite direct sum of indecomposable modules A i is continuous if and only if each A i is continuous and Aj -injective for all j ≠ i.