Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.

The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G? (G? is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).