Ideal Generated By $a_1, \ldots, a_n$, or $\left<a_1,a_2,\ldots,a_n\right>$

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Definition (Ideal Generated By $a_1, \ldots, a_n$, or $\left<a_1,a_2,\ldots,a_n\right>$)

Let $R$ be a commutative ring with unity, and let $a_1, \ldots, a_n \in R$. The set $I=\left<a_1,a_2,\ldots,a_n\right> = \{r_1a_1+\cdots +r_na_n|r_i\in R \}$ is called the ideal generated by $a_1, \ldots, a_n$. Any other ideal that contains $a_1, \ldots, a_n$ must contain $I$.

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