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# Article

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Keywords:
idempotent semiring; variety; Green relations; band; bisemilattice
Summary:
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.
References:
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[4] Sen M. K., Guo Y. Q., and K. P. Shum: A class of idempotent semirings. preprint. MR 1828821

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