Definition:Principal Left Ideal of Ring
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Definition
Let $\struct {R, +, \circ}$ be a ring with unity.
Let $a \in R$.
We define:
- $R a = \set {r \circ a : r \in R}$
The left ideal $Ra$ is called the principal left ideal of $R$ generated by $a$.
Also see
- Principal Left Ideal is Left Ideal: where it is shown that the principal left ideal $R a$ is a left ideal.
- Definition:Principal Right Ideal of Ring