ON SEMI-ARTINIAN WEAKLY CO-SEMISIMPLE MODULES t

We show that every semi-artinian module which is contained in a direct sum of finitely presented modules in sigma[M], is weakly co-semisimple if and only if it is regular in sigma[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.