FI-Extending Semimodule and Singularity

Samah  Alhashemi; Asaad M. A.  Alhossaini

doi:10.24996/ijs.2022.63.3.32

Authors

Samah Alhashemi College of Science for Women, University of Babylon, Babylon, Iraq
Asaad M. A. Alhossaini College of Education for Pure Sciences, Babylon University, Babylon, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.3.32

Keywords:

Semimodules, Fully Invariant Subsemimodule, FI-Extending Semimodule, Extending Semimodule, Singular Semimodule, Nonsingular Semimodul

Abstract

The main aim of this research is to present and to study several basic characteristics of the idea of FI-extending semimodules. The semimodule is said to be an FI-extending semimodule if each fully invariant subsemimodule of is essential in direct summand of . The behavior of the FI-extending semimodule with respect to direct summands as well as the direct sum is considered. In addition, the relationship between the singularity and FI-extending semimodule has been studied and investigated. Finally extending propertywhich is stronger than FI extending, that has some results related to FI-extending and singularity is also investigated.