Abstract:
In this thesis, we study 2-absorbing, weakly 2-absorbing, AG2-absorbing and weakly AG2-absorbing subsemimodules of semimodules over commutative semirings. Those are extended from prime, weakly prime, primary and weakly primary subsemimodules, respectively. Some characterizations of 2-absorbing, weakly 2-absorbing, AG2-absorbing and weakly AG2-absorbing subsemimodules are obtained. Moreover, we investigate relationships between 2-absorbing, weakly 2-absorbing, AG2-absorbing and weakly AG2-absorbing subsemimodules of semimodules over commutative semirings and 2-absorbing, weakly 2-absorbing, AG2-absorbing and weakly AG2-absorbing ideals of the same semirings. Finally, we obtain necessary and sufficient conditions of a semimodule in order to be a top semimodule.
