Title: On several classes of additively non-regular $C$-semirings
Abstract: In this paper, the authors study several classes of additively non-regular C-semirings whose additive idempotents are central, including the generalized C-rpp semirings, C-rpp semirings, generalized C-abundant semirings and C-abundant semirings.After introducing the concept of generalized C-rpp semirings, the authors obtain their equivalent characterizations, and show that a semiring is a generalized C-rpp semiring if and only if it is a strong b-lattice of additively left cancellative halfrings, and if and only if it is a subdirect product of a b-lattice and an additively left cancellative halfring.Also, the authors give the constructions of C-rpp semirings, generalized C-abundant semirings and C-abundant semirings.Consequently, the corresponding results of Clifford semirings and generalized Clifford semirings in [7] and [29] are extended and generalized.