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On the Decomposition of Nonsingular CS-Modules

Published online by Cambridge University Press:  20 November 2018

John Clark  and
Nguyen Viet Dung
John Clark
Affiliation:
Department of Mathematics andStatistics, University of Otago, PO Box 56, Dunedin, New Zealand, e-mail:[email protected]
Nguyen Viet Dung
Affiliation:
Institute of Mathematics, P.O. Box 631 Bo Ho, Hanoi, Vietnam, e-mail:[email protected]
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Abstract

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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.

Keywords

Primary: 16D70secondary: 16D4016D5016D80nonsingular moduleCS-moduleindecomposable modulequasi-injective moduleuniserial modulehereditary ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 257 - 265
Copyright
Copyright © Canadian Mathematical Society 1996

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