M. Hamidi - Department of Mathematics, Payame Noor University (PNU), P.O. Box ۱۹۳۹۵- ۴۶۹۷, Tehran, Iran.
F. Faraji - Department of Mathematics, Payame Noor University (PNU), P.O. Box ۱۹۳۹۵- ۴۶۹۷, Tehran, Iran.
R. Ameri - School of Mathematics, Statistics and Computer Sciences, University of Tehran, P.O. Box ۱۴۱۵۵-۶۴۵۵, Tehran, Iran.
Kh. Ahmadi-amoli - Department of Mathematics, Payame Noor University (PNU), P.O. Box ۱۹۳۹۵- ۴۶۹۷, Tehran, Iran.

In this paper, we construct the concept of general  Krasner  hyperring based on the  ring  structures and the left general Krasner hypermodule based on the  module structures.  This study introduces  the  trivial left general Krasner hypermodules and  proves that the  trivial left general Krasner   hypermodules  are  different from left  Krasner   hypermodules. We show that for any given general  Krasner  hyperring R and trivial left general Krasner   hypermodules A, B, {\bf_{R}h}om(A, B) is a left general Krasner   hypermodule and  {\bf_{R}h}om(-, B),     ({\bf_{R}h}om(A, -) ) is an   exact covariant functor (contravariant). Finally, we  show that the category {\bf_{R}GKH}mod (left  trivial general Krasner hypermodules and all (homomorphisms) is an abelian  category and  trivial left general Krasner hypermodules have  a normal injective resolution.

Keywords: General Krasner hyperrings, (normal injective) left general Krasner hypermodules, normal injective resolution, abelian category