Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $S$.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph