|
In commutative algebra, a system of parameters for a local ring of Krull dimension ''d'' with maximal ideal ''m'' is a set of elements ''x''1, ..., ''x''''d'' that satisfies any of the following equivalent conditions: # ''m'' is a minimal prime of (''x''1, ..., ''x''''d''). # The radical of (''x''1, ..., ''x''''d'') is ''m''. # Some power of ''m'' is contained in (''x''1, ..., ''x''''d''). # (''x''1, ..., ''x''''d'') is ''m''-primary. Every local Noetherian ring admits a system of parameters. It is not possible for fewer than ''d'' elements to generate an ideal whose radical is ''m'' because then the dimension of ''R'' would be less than ''d''. If ''M'' is a ''k''-dimensional module over a local ring, then ''x''1, ..., ''x''''k'' is a system of parameters for ''M'' if the length of is finite. ==References== * 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「system of parameters」の詳細全文を読む スポンサード リンク
|