In this paper, we give a generalization of slightly compressible modules. We introduce the notion of M-slightly compressible modules, i.e. a right R module N is called M-slightly compressible if for every nonzero submodule A of N there exists a nonzero R-homomorphism s from M to N such that ↪ . Many examples of M-slightly compressible modules are provided. Some results on M-slightly compressible modules are obtained, which are interesting and important.
Abstract. In this paper, we introduce the concept of slightly compressible-injective modules, following this, a right R-module N is called an M -slightly compressible-injective module, if every R-homomorphism from a non-zero M -slightly compressible submodule of M to N can be extended to M . We give some characterizations and properties of slightly compressible-injective modules.
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