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\title{Weakly Prime Ideals}
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\put(6.6,-0.0){ \Large{\textbf{$88^{th}$ Iranian Analisis Seminar} }}
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{\definition
For $I$ as an ideal of $R$, we define
\begin{itemize}
\item[$(1)$] $I$ is  prime if $a,b\in R$ with $a$ implies that $a\in I$ or $b\in I$ \cite{Anderson,Sharma};
\item[$(2)$]  then there are $n$
of the $a_i$'s whose product is in $I$ \cite{Anderson1};
\item[$(3)$] $I$ 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 $I$ \cite{Nekooei};
\end{itemize}}
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{\theorem
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.}\label{product}
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The following theorem follows from Theorem \ref{product}.