Clifford semirings and generalized Clifford semirings

It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. In this paper, we extend this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. Also, as a further generalization, we prove that a semiring S is a genneralized Clifford semiring if and only if S is a strong b-lattice of skew-rings. Some results which have been recently obtained in the literature [2] are strengthened and extended.