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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 961–966, July, 2013.
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Nebiyev, C., Pancar, A. On Supplement Submodules. Ukr Math J 65, 1071–1078 (2013). https://doi.org/10.1007/s11253-013-0842-2
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DOI: https://doi.org/10.1007/s11253-013-0842-2