On Supplement Submodules

  • C. Nebiyev
  • A. Pancar Ondokuz Mayis Univ., Turkey


We investigate some properties of supplement submodules. Some relations between lying-above and weak supplement submodules are also studied. Let V be a supplement of a submodule U in M. Then it is possible to define a bijective map between the maximal submodules of V and the maximal submodules of M that contain U. Let M be an R-module, U ≤ M, let V be a weak supplement of U, and let K ≤ V. In this case, K is a weak supplement of U if and only if V lies above K in M. We prove that an R-module M is amply supplemented if and only if every submodule of M lies above a supplement in M. We also prove that M is semisimple if and only if every submodule of M is a supplement in M.
How to Cite
NebiyevC., and PancarA. “On Supplement Submodules”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 7, July 2013, pp. 961–966, http://umj.imath.kiev.ua/index.php/umj/article/view/2481.
Research articles