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Graph Monoids.

F.W. Roush, K.H. Kim, L.G. Makar-Limanov (1982)

Semigroup forum

Green’s 𝒟 -relation for the multiplicative reduct of an idempotent semiring

Francis J. Pastijn, Xian Zhong Zhao (2000)

Archivum Mathematicum

The idempotent semirings for which Green’s 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 𝒟 -relation on the multiplicative reduct is the least lattice congruence.

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