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A principal ideal is an ideal ''I'' in a ring ''R'' that is generated by a single element ''a'' of ''R'' through multiplication by every element of ''R''. ==Definitions== * a ''left principal ideal'' of ''R'' is a subset of ''R'' of the form ''Ra'' = ; * a ''right principal ideal'' is a subset of the form ''aR'' = ; * a ''two-sided principal ideal'' is a subset of the form ''RaR'' = . If ''R'' is a commutative ring, then the above three notions are all the same. In that case, it is common to write the ideal generated by ''a'' as ⟨''a''⟩. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「principal ideal」の詳細全文を読む スポンサード リンク
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