Semiring

Summary

A semiring is a set with an addition and a multiplication that obey the axioms of a ring, except that negatives need not exist. The natural numbers with the usual operations are the first example. Every ring is a semiring, but semirings also include the Boolean semiring and the tropical semirings. Semirings appear in combinatorics, in tropical geometry and in computer science, for example in shortest path problems and formal languages.