Category:Ideals of Rings

This category contains results about Ideals of Rings.
Definitions specific to this category can be found in Definitions/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:

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