Ideals in Semirings

Abstract

Ideals play a fundamental role in ring theory and it is therefore natural to consider them also in the context of semiring theory. Here their role is no less important, though we will often have to restrict our consideration to special types of ideals. In particular, we will show that, as in the case of rings, the family of all ideals of a semiring is, in a natural way, a semiring. Formally, the definitions in the two situations are the same.