# Category:Examples of Ideals of Rings

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This category contains examples of **Ideal of Ring**.

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 "Examples of Ideals of Rings"

The following 6 pages are in this category, out of 6 total.

### I

- Ideal of Ring/Examples
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries/Corollary
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries/Proof 1
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries/Proof 2
- Ideal of Ring/Examples/Set of Even Integers