Definition:Principal Right Ideal of Ring

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

Let $a \in R$.

We define:
 * $aR = \ds \set {a \circ r : r \in R}$

The right ideal $aR$ is called the right principal ideal of $R$ generated by $a$.

Also see

 * User:Leigh.Samphier/Sandbox/Right Principal Ideal is Right Ideal: where it is shown that the right principal ideal $aR$ is a right ideal.
 * User:Leigh.Samphier/Sandbox/Definition:Left Principal Ideal of Ring