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In commutative algebra, a ring of mixed characteristic is a commutative ring having characteristic zero and having an ideal such that has positive characteristic.〔.〕 == Examples == * The integers have characteristic zero, but for any prime number , is a finite field with elements and hence has characteristic . * The ring of integers of any number field is of mixed characteristic * Fix a prime ''p'' and localize the integers at the prime ideal (''p''). The resulting ring Z(''p'') has characteristic zero. It has a unique maximal ideal ''p''Z(''p''), and the quotient Z(''p'')/''p''Z(''p'') is a finite field with ''p'' elements. In contrast to the previous example, the only possible characteristics for rings of the form are zero (when ''I'' is the zero ideal) and powers of ''p'' (when ''I'' is any other non-unit ideal); it is not possible to have a quotient of any other characteristic. * If is a non-zero prime ideal of the ring of integers of a number field then the localization of at is likewise of mixed characteristic. * The ''p''-adic integers Z''p'' for any prime ''p'' are a ring of characteristic zero. However, they have an ideal generated by the image of the prime number ''p'' under the canonical map . The quotient Z''p''/''p''Z''p'' is again the finite field of ''p'' elements. Z''p'' is an example of a complete discrete valuation ring of mixed characteristic. * The integers, the ring of integers of any number field, and any localization or completion of one of these rings is a characteristic zero Dedekind domain. 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「ring of mixed characteristic」の詳細全文を読む スポンサード リンク
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