Generalized fuzzy -ideals of semirings with interval-valued membership functions.
Generalized quotients of hemirings
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.
Green's relations in a semiring