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Characterizing rings by a direct decomposition property of their modules

Published online by Cambridge University Press:  09 April 2009

Dinh Van Huynh
Department of Mathematics, Ohio University, Athens, Ohio 45701, USA, e-mail:
S. Tariq Rizvi
Department of Mathematics, The Ohio State University at Lima, Lima, Ohio 45804, USA, e-mail:
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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.

Research Article
Copyright © Australian Mathematical Society 2006


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