On Supplement Submodules
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 7, pp 1071-1078.
Citation Example: Nebiyev C., Pancar A. On Supplement Submodules // Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 961–966.