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In mathematics, the ''i''th Bass number of a module ''M'' over a local ring ''R'' with residue field ''k'' is the ''k''-dimension of Ext(''k'',''M''). More generally the Bass number μ''i''(''p'',''M'') of a module ''M'' over a ring ''R'' at a prime ideal ''p'' is the Bass number of the localization of ''M'' for the localization of ''R'' (with respect to the prime ''p''). Bass numbers were introduced by . The Bass numbers describe the minimal injective resolution of a finitely-generated module ''M'' over a Noetherian ring: for each prime ideal ''p'' there is a corresponding indecomposable injective module, and the number of times this occurs in the ''i''th term of a minimal resolution of ''M'' is the Bass number μ''i''(''p'',''M''). ==References== * * http://arxiv.org/abs/math/0010003 * 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「Bass number」の詳細全文を読む スポンサード リンク
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