Kaeden Hoffman
2022-07-10
Answered

Just a simple question. What does Eisenbud mean by $(x:y)$ where $x,y\in R$ a ring. An example on this is in the section 17 discussing the homology of the koszul complex. I assume it's something along the lines of $\{r\mid ax=ry\}$ for some $a\in R$.

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Jamiya Costa

Answered 2022-07-11
Author has **18** answers

Eisenbud introduces this notation in section 0.3. If $I$ and $J$ are two ideals in $R$, then

$(I:J)=\{r\in R\mid r\cdot J\subseteq I\}.$

In this case, $I=(x)$, $J=(y)$.

$(I:J)=\{r\in R\mid r\cdot J\subseteq I\}.$

In this case, $I=(x)$, $J=(y)$.

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