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Let $\mathcal{S}$ be a finite commutative semigroup. The Davenport constantof $\mathcal{S}$, denoted $D(\mathcal{S})$, is defined to be the least positiveinteger $d$ such that every sequence $T$ of elements in $\mathcal{S}$ of lengthat least $d$ contains a subsequence $T'$ with the sum of all terms from $T'$equaling the sum of all terms from $T$. Let $\F_p[x]$ be a polynomial ring inone variable over the prime field $\F_p$, and let $f(x)\in \F_p[x]$. In thispaper, we made a study of the Davenport constant of the multiplicativesemigroup of the quotient ring $\frac{\F_p[x]}{\langle f(x)\rangle}$. Amongother results, we mainly prove that, for any prime $p>2$ and any polynomial$f(x)\in \F_p[x]$ which can be factorized into several pairwise non-associtedirreducible polynomials in $\F_p[x]$, then$$D(\mathcal{S}_{f(x)}^p)=D(U(\mathcal{S}_{f(x)}^p)),$$ where$\mathcal{S}_{f(x)}^p$ denotes the multiplicative semigroup of the quotientring $\frac{\F_p[x]}{\langle f(x)\rangle}$ and $U(\mathcal{S}_{f(x)}^p)$denotes the group of units of the semigroup $\mathcal{S}_{f(x)}^p$.

Davenport constant of the multiplicative semigroup of the quotient ring $\frac{\F_p[x]}{\langle f(x)\rangle}$