Submodul Maksimal Bertingkat Terdekomposisi pada Modul Bertingkat

Abstract

Given  be a group with identity , and graded ring  type . By the graded ring can be formed graded module. A module  is called to be a graded module over graded ring  type  if there is family of subgroups of , say , for all  such that  and . The concepts of maximal submodule can also be defined in graded module. The graded proper submodule  of  is said to be a graded maximal if there is no graded other submodule that contains  properly except  itself. Not only usual module can be decomposed, but also graded module can be decomposed. This research discusses about graded modules with decomposed graded maximal submodules. By the decomposition, we obtain some properties that relate with graded maximal submodule, graded simple module, graded module homomorphism, graded torsion module, and graded direct summand.