Definition:Generated Ideal of Ring/Definition 2

Definition

Let $R$ be a commutative ring with unity.

Let $S \subseteq R$ be a subset.

The ideal generated by $S$ is the set of all linear combinations of elements of $S$.

Also see

• Equivalence of Definitions of Generated Ideal of Ring

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields