FI-Extending Semimodule and Singularity

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.

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Published

2022-03-30

How to Cite

Alhashemi, S. ., & Alhossaini, A. M. A. . (2022). FI-Extending Semimodule and Singularity. Iraqi Journal of Science, 63(3), 1277–1284. https://doi.org/10.24996/ijs.2022.63.3.32

Issue

Section

Mathematics