The concept of semi-essential semimodule has been studied by many researchers.
In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule is prime, then is fully prime. If every semi-essential subsemimodule of -semimodule is essential then is fully essential. Finally, a prime subsemimodule of is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule in , if , and whenever with is a prime subsemimodule in , , then . Furthermore, some results about the above concepts have been mentioned.
