On 2-absorbing ideals of commutative semirings

In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if \(\mathfrak{a}\) is a nonzero proper ideal of a subtractive valuation semiring \(S\) then \(\mathfrak{a}\) is a 2-absorbing ideal of \(S\) if and only if \(\mathfrak{a}=\mathfrak{p}\) or \(\mathfrak{a}=\mathfrak{p}^2\) where \(\mathfrak{p}=\sqrt\mathfrak{a}\) is a prime ideal of \(S\). We also show that each 2-absorbing ideal of a subtractive semiring \(S\) is prime if and only if the prime ideals of \(S\) are comparable and if \(\mathfrak{p}\) is a minimal prime over a 2-absorbing ideal \(\mathfrak{a}\), then \(\mathfrak{am} = \mathfrak{p}\), where \(\mathfrak{m}\) is the unique maximal ideal of \(S\).