In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if a is a nonzero proper ideal of a subtractive valuation semiring S then a is a 2-absorbing ideal of S if and only if a = p or a = p 2 where p = √ 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 p is a minimal prime over a 2-absorbing ideal a, then am = p, where m is the unique maximal ideal of S.2010 Mathematics Subject Classification. 16Y60; 13A15.

A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring [Formula: see text] is uniserial if and only if the matrix semiring [Formula: see text] is uniserial. As a generalization of valuation semirings, we also investigate those semirings whose prime ideals are linearly ordered by inclusion. For example, we prove that the prime ideals of a commutative semiring [Formula: see text] are linearly ordered if and only if for each [Formula: see text], there is a positive integer [Formula: see text] such that either [Formula: see text] or [Formula: see text]. Then, we introduce and characterize pseudo-valuation semidomains. It is shown that prime ideals of pseudo-valuation semidomains and also of the divided ones are linearly ordered.