Abstract Let $S$ be a commutative semiring and $T(S)$ be
the set of all ideals of $S$. Let $\phi\:T(S)\to T(S)\cup
\{\emptyset\}$ be a function. A proper ideal $I$ of a semiring
$S$ is called an $(n-1,n)$-$\phi$-prime ideal of $S$ if
$a_{1}a_{2}\cdots a_{n}\in I\setminus \phi(I)$,
$a_{1},a_{2},\dots,a_{n}\in S$ implies that $a_{1}a_{2}\cdots
a_{i-1}a_{i+1}\cdots a_{n}\in I$ for some $i\in \{1,2,\dots,n\}$.
In this paper, we prove several results concerning
$(n-1,n)$-$\phi$-prime ideals in a commutative semiring $S$ with
non-zero identity connected with those in commutative ring theory. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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