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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