J. Aust. Math. Soc.  80 (2006), 359-366
Characterizing rings by a direct decomposition property of their modules

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


Abstract
A module $M$ is said to satisfy the condition $(\wp^*)$ 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 $(\wp^*)$, 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 $(\wp^*)$ is also left artinian, but the property $(\wp^*)$ is not left-right symmetric.
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