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Principal ideal : ウィキペディア英語版
Principal ideal

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)
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