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Characterizing rings by a direct decomposition property of their modules

Part of: Chain conditions, growth conditions, and other forms of finiteness Modules, bimodules and ideals

Published online by Cambridge University Press:  09 April 2009

Dinh Van Huynh  and
S. Tariq Rizvi
Dinh Van Huynh
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701, USA, e-mail: huynh@math.ohiou.edu
S. Tariq Rizvi
Affiliation:
Department of Mathematics, The Ohio State University at Lima, Lima, Ohio 45804, USA, e-mail: rizvi.1@osu.edu
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Abstract

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A module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation 16P20: Artinian rings and modules 16D50: Injective modules, self-injective rings

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 3 , June 2006 , pp. 359 - 366
Copyright
Copyright © Australian Mathematical Society 2006

References

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