Large-maximal small submodules

Abstract

In this study, the ideas of Large-maximal small submodules and Large-maximal small radical of modules are presented. The primary attributes and features of the concept of large-maximal small submodules are provided. Additionally, we discuss the connections between this idea and various submodule kinds with the help of examples and observations that are relevant to our work. Where a proper submodule A of a T-module G is said to be Large-maximal small submodule, if A + B = G where B is a proper submodule of G, then B is Large-Maximal submodule of G. A Large-maximal small radical of module is the sum of all Large-maximal small submodule in G. It will be studied how this concept of radicality relates to other radical conceptions.