Communications of the
Korean Mathematical Society CKMS

In this paper, we present different 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 submodules, graded Jacobson radical, gr-Jacobson radical, gr-max-nested modules, decomposition

MSC numbers: 13A02