[[Ring theory MOC]]
# Principal ideal ring

A (left/right/two-sided) **principal ideal ring** or **PIR** $R$ is a [[ring]] in which every (left/right/two-sided) [[ideal]] is [[Principal ideal|principal]]. #m/def/ring 
Clearly every (left/right/two-sided) PIR is a [[Noetherian ring]].

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#state/tidy | #lang/en | #SemBr