Xianzhong Zhao, Department of Mathematics, Zhong Shan University, Guangzhou 510275, People's Republic of China
Abstract. The idempotent semiring s for which Green's $\CD$-relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the $\Cal D$-relation on the multiplicative reduct is the least lattice congruence.
AMSclassification. 16Y60, 20M10
Keywords. Idempotent semiring, variety, Green relations, band, bisemilattice