Hybrid structures applied to modules over semirings

The concept of a hybrid structure in X-semimodules, where X is a semiring, is introduced in this paper. The notions of hybrid subsemimodule and hybrid right (resp., left) ideals are defined and discussed in semirings. We investigate the representations of hybrid subsemimodules and hybrid ideals using hybrid products. We also get some interesting results on t-pure hybrid ideals in X. Furthermore, we show how hybrid products and hybrid intersections are linked. Finally, the characterization theorem is proved in terms of hybrid structures for fully idempotent semirings.