Decompositions of Graded Maximal Submodules Commun. Korean Math. Soc. Published online March 5, 2021 Fida Moh'd Princess Sumaya University for Technology Abstract : In this paper, we present diff erent decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems. Keywords : graded rings, graded modules, graded maximal submodules, gr-maximal sub- modules, graded Jacobson radical, gr-Jacobson radical, gr-max-nested modules, decomposition MSC numbers : 13A02 Full-Text :