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On the Decomposition of Continuous Modules
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove two theorems on continuous modules: Decomposition Theorem. A continuous module M has a decomposition, M = M1 ⊕ M2, such that M1 is essential over a direct sum of indecomposable summands Ai of M, and M2 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 Ai is continuous if and only if each Ai is continuous and Aj-injective for all j ≠ i.
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- Copyright © Canadian Mathematical Society 1982
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