s-Compressible and s-Prime Modules

Asaad M. A.  Alhossaini

doi:10.24996/ijs.2022.63.3.25

Authors

Asaad M. A. Alhossaini Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq https://orcid.org/0000-0002-4569-3352

DOI:

https://doi.org/10.24996/ijs.2022.63.3.25

Keywords:

critically s-compressible module, retractable module s-compressible module, s-rime module, small submodule

Abstract

Let R be a ring with identity and Ą a left R-module. In this article, we introduce new generalizations of compressible and prime modules, namely s-compressible module and s-prime module. An R-module A is s-compressible if for any nonzero submodule B of A there exists a small f in Hom_R(A, B). An R-module A is s-prime if for any submodule B of A, ann_R (B) A is small in A. These concepts and related concepts are studied in as well as many results consist properties and characterizations are obtained.