# Category:Definitions/Ideals of Rings

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This category contains definitions related to Ideals of Rings.

Related results can be found in Category:Ideals of Rings.

Let $\struct {R, +, \circ}$ be a ring.

Let $\struct {J, +}$ be a subgroup of $\struct {R, +}$.

Then $J$ is an **ideal of $R$** if and only if:

- $\forall j \in J: \forall r \in R: j \circ r \in J \land r \circ j \in J$

that is, if and only if:

- $\forall r \in R: J \circ r \subseteq J \land r \circ J \subseteq J$

## Pages in category "Definitions/Ideals of Rings"

The following 2 pages are in this category, out of 2 total.