\end{center}

\vskip .2 in


\newcommand{\A}{\mathbb{N}_0}
\newcommand{\ber}{\mathcal{B}}
\newcommand{\eulr}{\mathcal{E}}
\newcommand{\s}{\mathcal{S}}

\begin{abstract}
The Cauchy-type product of two arithmetic functions $f$ and $g$ on
nonnegative integers is defined by $(f\bullet g)(k):=\sum_{m=0}^{k}
{k\choose m}f(m)g(k-m)$.  We explore some algebraic properties of the
aforementioned convolution, which is a fundamental characteristic of
the identities involving the Bernoulli numbers, the Bernoulli
polynomials, the power sums, the sums of products,  and so forth.
\end{abstract}