ALGEBRA COLLOQUIUM, vol.14, no.4, pp.625-630, 2007 (SCI-Expanded)
A module M is called circle plus-supplemented if every submodule of M has a supplement that is a direct summand of M. It is shown that if M is a circle plus-supplemented module and r(M) is a coclosed submodule of M for a left preradical r, then r(M) is a direct summand of M, and both r(M) and M/r(M) are circle plus-supplemented.