A right continuous right weakly si-ring is semisimple
Published online by Cambridge University Press: 17 April 2009
It is shown that a projective CS right module M over a ring R is a direct sum of uniform modules of composition lengths at most 2 if (i) every finitely generated direct summand of M is continuous and (ii) every non-zero M-singular right R-module contains a non-zero M-injective submodule. In particular, a right continuous ring R is semisimple if R is right weakly SI, that is, if every non-zero singular right R-module contains a non-zero injective submodule.
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