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On the Decomposition of Continuous Modules

Published online by Cambridge University Press:  20 November 2018

Bruno J. Müller  and
S. Tariq Rizvi
Bruno J. Müller
Affiliation:
McMaster University, Hamilton, Ontario, Canada
S. Tariq Rizvi
Affiliation:
University of Waterloo, Waterloo, Ontario
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Abstract

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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.

Keywords

16A52
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 296 - 301
Copyright
Copyright © Canadian Mathematical Society 1982

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