Completely regular R-semirings and completely regular L-semirings

In [6] it was shown that a semiring is completely regular semiring if and only if it is a b-lattice of completely simple semirings. In this paper, we generalize this concept and introduce completely regular R-semiring, completely regular L-semiring and we show that a semiring is completely regular semiring if and only if it is both a completely regular L-semiring and a completely regular R-semiring. Moreover, we show that a semiring is a completely regular R-semiring (completely regular L-semiring) if and only if it is a b-lattice of completely simple R-semirings (completely simple L-semirings).