General form of slightly compressible modules

Abstract

In this thesis, we determine a general form of slightly compressible modules. Let R be an associative ring with identity and M a right R-module. A right R-module N is called an M-slightly compressible module if, for every nonzero submodule A of N, there exists a nonzero R-module homomorphism from M to A. In the case that M = N, N is, in fact, a slightly compressible module. Moreover, we provide conditions for any right R-module to be an M-slightly compressible module and study some properties of M-slightly compressible modules. Next, we introduce the concept of M-slightly compressible injective modules. A right R-module N is called an M-slightly compressible injective module if every R-module homomorphism from an M-slightly compressible submodule of M to N can be extended to M. Moreover, we study some properties of M-slightly compressible injective modules and also provide examples of them. Finally, we introduce the concept of sub-M-principally injective modules. A right R-module N is called a sub-M-principally injective madule if for any nonzero submodule A of M, any R-module homomorphism from A-cyclic submodule of A to N can be extended to M. Moreover, we study some properties of sub-M-principally injective modules and also provide examples of them.