Category:Definitions/Generators of Ideals

This category contains definitions related to Generators of Ideals.
Related results can be found in Category:Generators of Ideals.

Let $R$ be a commutative ring.

Let $I \subset R$ be an ideal.

Let $S \subset I$ be a subset.

Then:

$S$ is a generator of $I$

if and only if:

$I$ is the ideal generated by $S$.