Tagged: ideal quotient

Ideal Quotient (Colon Ideal) is an Ideal

Problem 203

Let $R$ be a commutative ring. Let $S$ be a subset of $R$ and let $I$ be an ideal of $I$.
We define the subset
\[(I:S):=\{ a \in R \mid aS\subset I\}.\] Prove that $(I:S)$ is an ideal of $R$. This ideal is called the ideal quotient, or colon ideal.

 
Read solution

LoadingAdd to solve later