  A semiring is uniserial if its ideals are totally ordered by inclusion.
First, we show that a semiring $S$ is uniserial if and only if the matrix
semiring $M_n(S)$ 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 $S$ are linearly ordered if and only if for each $x,y \in S$, there is
a positive integer $n$ such that either $x|y^n$ or $y|x^n$. 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.
