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Unverified Commit 33ff043f authored by rrueger's avatar rrueger
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Algebra I: Commutative Rings. Compact definition of ideal

parent 18f43972
...@@ -397,9 +397,9 @@ ...@@ -397,9 +397,9 @@
An \textbf{ideal} in a commutative ring $R$ is a subset $I$ of $R$ such that An \textbf{ideal} in a commutative ring $R$ is a subset $I$ of $R$ such that
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\begin{enumerate} \begin{enumerate}
\item $0 \in I$, \item $(I, +, 0) \subseteq R$ is a group
\item if $a,b \in I$, then $a + b \in I$, \item $I$ is closed under multiplication from elements in $R$, i.e\ for $r
\item if $a \in I$ and $r \in R$, then $ra \in I$. \in R, a \in I: ra \in I$
\end{enumerate} \end{enumerate}
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The ring $R$ itself and $(0)$, the subset containing only $0$, are always The ring $R$ itself and $(0)$, the subset containing only $0$, are always
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