Definition:Principal Left Ideal of Ring

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

Let $a \in R$.

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

The left ideal $Ra$ is called the left principal ideal of $R$ generated by $a$.

Also see

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