TITLE: Question on notation from Eisenbud's Commutative algebra - (x:y)
QUESTION [1 upvotes]: 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 $a \in R$.

REPLY [2 votes]: 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, $I = (x)$, $J = (y)$.
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