Document Type: Research Paper
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.