Editing Principal ideal (section)

{{Short description|Ring ideal generated by a single element of the ring}}
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In [[mathematics]], specifically [[ring theory]], a '''principal ideal''' is an [[ideal (ring theory)|ideal]] <math>I</math> in a [[ring (mathematics)|ring]] <math>R</math> that is generated by a single element <math>a</math> of <math>R</math> through multiplication by every element of <math>R.</math> The term also has another, similar meaning in [[order theory]], where it refers to an [[ideal (order theory)|(order) ideal]] in a [[poset]] <math>P</math> generated by a single element <math>x \in P,</math> which is to say the set of all elements less than or equal to <math>x</math> in <math>P.</math>

The remainder of this article addresses the ring-theoretic concept.