On commutative FGI-Rings.

M. Barry; C. T. Gueye; M. Sanghare

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On some properties of $\oplus$ -supplemented modules.

Idelhadj, A., Tribak, R. (2003)

International Journal of Mathematics and Mathematical Sciences

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Rings whose modules have maximal submodules.

Carl Faith (1995)

Publicacions Matemàtiques

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A ring R is a right max ring if every right module M ≠ 0 has at least one maximal submodule. It suffices to check for maximal submodules of a single module and its submodules in order to test for a max ring; namely, any cogenerating module E of mod-R; also it suffices to check the submodules of the injective hull E(V) of each simple module V (Theorem 1). Another test is transfinite nilpotence of the radical of E in the sense that rad^α E = 0;...