ALGEBRA COLLOQUIUM, vol.24, no.4, pp.603-610, 2017 (SCI-Expanded)
We are interested in studying when the class of local modules is Baer-Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S-1 and S-2 such that the rings End(R)(S-1) and End(R)(S-2) are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer-Kaplansky if and only if so is the class of simple R-modules.