Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the arithmetic of polynomial semidomains   A subset $S$ of an integral domain $R$ is called a semidomain provided that
the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities. The study of
factorizations in integral domains was initiated by D. D. Anderson, D. F.
Anderson, and M. Zafrullah in 1990, and this area has been systematically
investigated since then. In this paper, we study the divisibility and
arithmetic of factorizations in the more general context of semidomains. We are
specially concerned with the ascent of the most standard divisibility and
factorization properties from a semidomain to its semidomain of (Laurent)
polynomials. As in the case of integral domains, here we prove that the
properties of satisfying ACCP, having bounded factorizations, and having finite
factorizations ascend in the class of semidomains. We also consider the ascent
of the property of being atomic, and we show that the property of having unique
factorization ascends only when a semidomain is an integral domain. Throughout
the paper we provide several examples aiming to shed some light upon the
arithmetic of factorizations of semidomains.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph