Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A problem of Wang on Davenport constant for the multiplicative semigroup
  of the quotient ring of $\F_2[x]$   Let $\F_q[x]$ be the ring of polynomials over the finite field $\F_q$, and
let $f$ be a polynomial of $\F_q[x]$. Let $R=\frac{\F_q[x]}{(f)}$ be a quotient
ring of $\F_q[x]$ with $0\neq R\neq \F_q[x]$. Let $\mathcal{S}_R$ be the
multiplicative semigroup of the ring $R$, and let ${\rm U}(\mathcal{S}_R)$ be
the group of units of $\mathcal{S}_R$. The Davenport constant ${\rm
D}(\mathcal{S}_R)$ of the multiplicative semigroup $\mathcal{S}_R$ is the least
positive integer $\ell$ such that for any $\ell$ polynomials
$g_1,g_2,\ldots,g_{\ell}\in \F_q[x]$, there exists a subset $I\subsetneq
[1,\ell]$ with $$\prod\limits_{i\in I} g_i \equiv \prod\limits_{i=1}^{\ell}
g_i\pmod f.$$ In this manuscript, we proved that for the case of $q=2$, $${\rm
D}({\rm U}(\mathcal{S}_R))\leq {\rm D}(\mathcal{S}_R)\leq {\rm D}({\rm
U}(\mathcal{S}_R))+\delta_f,$$ where \begin{displaymath}
\delta_f=\left\{\begin{array}{ll} 0 & \textrm{if $\gcd(x*(x+1_{\mathbb{F}_2}),\
f)=1_{\F_{2}}$}\\ 1 & \textrm{if $\gcd(x*(x+1_{\mathbb{F}_2}),\ f)\in \{x, \
x+1_{\mathbb{F}_2}\}$}\\ 2 & \textrm{if
$gcd(x*(x+1_{\mathbb{F}_2}),f)=x*(x+1_{\mathbb{F}_2}) $}\\ \end{array} \right.
\end{displaymath} which partially answered an open problem of Wang on Davenport
constant for the multiplicative semigroup of $\frac{\F_q[x]}{(f)}$ (G.Q. Wang,
\emph{Davenport constant for semigroups II,} Journal of Number Theory, 155
(2015) 124--134).

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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph