Definition:Principal Right Ideal of Ring
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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 principal right ideal of $R$ generated by $a$.
Also see
- Principal Right Ideal is Right Ideal: where it is shown that the principal right ideal $aR$ is a right ideal.
- Definition:Principal Left Ideal of Ring