Green's $\CD$-relation for the multiplicative reduct of an idempotent semiring

Francis Pastijn and Xianzhong Zhao

Address. F. Pastijn, Department of Mathematics, Statistics, and Computer Science, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881, USA

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