Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero-divisor graphs of nilpotent-free semigroups   We find strong relationships between the zero-divisor graphs of apparently
disparate kinds of nilpotent-free semigroups by introducing the notion of an
\emph{Armendariz map} between such semigroups, which preserves many
graph-theoretic invariants. We use it to give relationships between the
zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal
graph. Then we give relationships between the zero-divisor graphs of certain
topological spaces (so-called pearled spaces), prime spectra, maximal spectra,
tensor-product semigroups, and the semigroup of ideals under addition,
obtaining surprisingly strong structure theorems relating ring-theoretic and
topological properties to graph-theoretic invariants of the corresponding
graphs.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin