A theorem concerning the restriction of the -structure of a semigroup to a subsemigroup of
The maximal regular ideal of the semigroup of binary relations
Subsemigroups of completely simple semigroups. III.
Green’s -relation for the multiplicative reduct of an idempotent semiring
The idempotent semirings for which Green’s -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 -relation on the multiplicative reduct is the least lattice congruence.
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