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\title{Weakly Prime Ideals}
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\begin{definition}
For $I$ as an ideal of $R$, we define
\begin{enumerate}[\bf (1)]
\item $I$ is  prime if $a,b\in R$ with $a$ implies that $a\in I$ or $b\in I$ {\normalfont\cite{Anderson,Sharma}};
\item  then there are $n$
of the $a_i$'s whose product is in $I$ {\normalfont\cite{Anderson1}};
\item $I$ is  if whenever $backslash I^n$ for $a_,a_n \in R$, then there are $n$ of the $a_i$'s whose product is in $I$ {\normalfont\cite{Nekooei}};
\end{enumerate}
\end{definition}
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\begin{theorem}\label{product}
Let $R_{1}$ and $R_{2}$ are rings in which every proper ideal is a product of weakly prime ideals, then $R_{1}\times R_{2}$ also enjoys this property.
\end{theorem}

The following theorem follows from Theorem \ref{product}.

\begin{thebibliography}{00}
\bibitem{Anderson,Sharma}
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\bibitem{Anderson1}
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\bibitem{Nekooei}
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\bibitem{Anderson}
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\bibitem{Sharma}
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