The ideal theory in the quotients of semirings

Since the theory of ideals plays an important role in the theory of quotient semirings, in this paper, we will make an intensive study of the notions of Noetherian, Artinian, prime, primary, weakly primary and k-maximal ideals in commutative quotient semirings. The bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the residue class rings