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In algebra, the Mori–Nagata theorem introduced by and , states the following: let ''A'' be a noetherian reduced commutative ring with the total ring of fractions ''K''. Then the integral closure of ''A'' in ''K'' is a direct product of ''r'' Krull domains, where ''r'' is the number of minimal prime ideals of ''A''. The theorem is a partial generalization of the Krull–Akizuki theorem, which concerns a one-dimensional noetherian domain. A consequence of the theorem is that if ''R'' is a Nagata ring, then every ''R''-subalgebra of finite type is again a Nagata ring . The Mori–Nagata theorem follows from Matijevic's theorem. == 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「Mori–Nagata theorem」の詳細全文を読む スポンサード リンク
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