On Semi-artinian Weakly Co-semisimple Modules

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.


Volume 37, No. 3
September and October 2011
Pages 149-157
  • Receive Date: 28 November 2009
  • Revise Date: 15 March 2012
  • Accept Date: 15 February 2010