Category:Principal Ideal of Principal Ideal Domain is of Irreducible Element iff Maximal

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This category contains pages concerning Principal Ideal of Principal Ideal Domain is of Irreducible Element iff Maximal:


Let $\struct {D, +, \circ}$ be a principal ideal domain.

Let $\ideal p$ be the principal ideal of $D$ generated by $p$.


Then $p$ is irreducible if and only if $\ideal p$ is a maximal ideal of $D$.