On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules.

Two different notions of "essential" subsemimodules were introduced in the theory of semimodules over a semiring with identity, in order to generalize the same notion of "essential" submodules in the theory of modules over a ring with identity. In this paper, we introduce a new class of essential subsemimodules called weakly essential subsemimodules. We prove that this new class contains the others two kind of classes of "essential" subsemimodules. Futhermore, we studie the properties of weakly essential subsemimodules. For applications we introduce and investigate the co-hopfian semimodules with this new definition of semi-essential. [ABSTRACT FROM AUTHOR]