On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules (European Journal of Pure and Applied Mathematics, 2016)
Two different notions of "essential" subsemimodules were introducedin the theory of semimodules over a semiring with identity, in orderto generalize the same notion of "essential" submodules in thetheory of modules over a ring with identity.In this paper, we introduce a new class of essential subsemimodulescalled weakly essential subsemimodules. We prove that this new classcontains the others two kind of classes of "essential"subsemimodules. Futhermore, we studie the properties of weaklyessential subsemimodules. For applications we introduce andinvestigate the co-hopfian semimodules with this new definition ofsemi-essential.