The idempotent semirings for which Green’s ${\cal D}$-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.
@article{107721,
author = {Francis J. Pastijn and Xian Zhong Zhao},
title = {Green's $\mathcal{D}$-relation for the multiplicative reduct of an idempotent semiring},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {77-93},
zbl = {1051.16027},
mrnumber = {1761613},
language = {en},
url = {http://dml.mathdoc.fr/item/107721}
}
Pastijn, Francis J.; Zhao, Xian Zhong. Green's $\mathcal{D}$-relation for the multiplicative reduct of an idempotent semiring. Archivum Mathematicum, Tome 036 (2000) pp. 77-93. http://gdmltest.u-ga.fr/item/107721/
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