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On the Decomposition of Nonsingular CS-Modules

  • John Clark (a1) and Nguyen Viet Dung (a2)
Abstract

It is shown that if M is a nonsingular CS-module with an indecomposable decomposition M = ⊕ i∊I Mi , then the family {Mi | i € I} is locally semi-T"- nilpotent. This fact is used to prove that any nonsingular self-generator Σ-CS module is a direct sum of uniserial Noetherian quasi-injective submodules. As an application, we provide a new proof of Goodearl's characterization of non-singular rings over which all nonsingular right modules are projective.

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References
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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