Divisible hypermodules

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodule and based on it we introduce a new class of hypermodules, the one of divisible hypermodules. After presenting some of their fundamental properties, we will show that the class of normal injective R-hypermodules M and the class of divisible R-hypermodules M coincide whenever R is a hyperring with no zero-divisors over M. Finally, we answer to an open problem related to canonical hypergroups. In particular, we show that any canonical hypergroup can be endoweded with a ℤ-hypermodule structure and it is a normal injective ℤ-hypermodule if and only if it is a divisible ℤ-hypermodule.