t-Extending Krasner Hypermodules

Let M be a hypermodule over a hyperring R such that the intersection of any two subhypermodules of M is a subhypermodule of M. We introduce the concept of a t-essential subhypermodule in M relative to an arbitrary subhypermodule T of M, which is called T-t-essential subhypermodule of M. Our aim in this work is to investigate properties of t-essential subhypermodules. We apply this concept to introduce t-extending hypermodules. Examples are provided to illustrate different concepts.