Definition:Principal Ideal of Ring

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

Let $a \in R$.

We define:

$\ideal a = \ds \set {\sum_{i \mathop = 1}^n r_i \circ a \circ s_i: n \in \N, r_i, s_i \in R}$

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

Also see

  • Results about principal ideals can be found here.