On Baer-Kaplansky Classes of Modules

Tutuncu D., Tribak R.

ALGEBRA COLLOQUIUM, vol.24, no.4, pp.603-610, 2017 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1142/s1005386717000396
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.603-610
  • Hacettepe University Affiliated: Yes

Abstract

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.