Receive Date: 28 November 2009,
Revise Date: 15 March 2012,
Accept Date: 15 February 2010
Abstract
We show that every semi-artinian module which is contained in a
direct sum of
finitely presented modules in $si[M]$, is weakly co-semisimple if and only if it is regular in $si[M]$.
As a consequence, we observe that every
semi-artinian ring is regular in the sense of von Neumann if
and only if its simple modules are $FP$-injective.
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