The goal of this research is to introduce the concept of Large-maximal submodule, also we will consider some properties of it, such that a proper submodule N of an R-module M is said to be Large-maximal (L-maximal) submodule of M if there exists a submodule K of M such that N < K ≤ M, then K is essential submodule of M (K ≤e M).

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The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤e M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.

The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M  be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that  .

In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.