Source: wikibot/principal-ideal-ring
= Principal ideal ring
{wiki=Principal_ideal_ring}
A **principal ideal ring** (PIR) is a type of ring in which every ideal is a principal ideal. This means that for any ideal \\( I \\) in the ring \\( R \\), there exists an element \\( r \\in R \\) such that \\( I = (r) = \\\{ r \\cdot a : a \\in R \\\} \\). In other words, each ideal can be generated by a single element.