Definition:Generated Ideal of Ring/Definition 1

Definition

Let $R$ be a ring.

Let $S \subseteq R$ be a subset.

The ideal generated by $S$ is the smallest ideal of $R$ containing $S$, that is, the intersection of all ideals containing $S$.

Also see

• Equivalence of Definitions of Generated Ideal of Ring

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $22$. New Rings from Old
• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.3$: Some properties of subrings and ideals: Definition $2.14$