Generalized extending modules via exchange and clean properties


5th International Conference Noncommutative Rings and their Applications, Lens, France, 12 - 15 June 2017, vol.727, pp.201-210 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 727
  • Doi Number: 10.1090/conm/727/14635
  • City: Lens
  • Country: France
  • Page Numbers: pp.201-210
  • Hacettepe University Affiliated: Yes


A module is called extending or CS provided that every submodule is essential in a direct summand. There have been investigations of several generalized extending conditions in the literature. In this survey paper, we focus on the exchange property on some generalized extending modules. It is an open problem whether extending condition with exchange property implies cleanness or not. We mention some observations on the former problem to construct a counterexample as well as new type of open problems which are replaced by extending with generalized extending conditions.