An idempotent semiring:
dioid: Noun - (mathematics) An idempotent semiring.
In abstract algebra, a semiring is an algebraic structure. It is a generalization of a ring, dropping the requirement that each element must have an additive inverse.
At the same time, it is a generalization of bounded distributive lattices.
The term dioid (for "double monoid") has been used to mean semirings or other structures. It was used by Kuntzman in 1972 to denote a semiring.
It is alternatively sometimes used for naturally ordered semirings but the term was also used for idempotent subgroups by Baccelli et al. in 1992.
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