On 2-absorbing ideals of commutative semirings

Abstract

Let S be a commutative semiring with unity different than zero. In this paper, we study the concept of 2-absorbing ideals of S which can be considered as a generalization of prime ideals. Among others, it is shown that the radical of a 2-absorbing ideal is also a 2-absorbing ideal and there are at most 2 prime k-ideals of S that are minimal over a 2-absorbing ideals.