交換代數中,中山引理是相當有用的一個技術工具。

陳述

它的眾多等價陳述之一如下:

引理(中山正)。設為含單位元的交換為一理想為有限生成-。若,則存在滿足

推論

推論一。在上述條件下,若包含於Jacobson根,則必然有
推論二. 若的子模,且存在有限生成的的子模及包含於Jacobson根的理想,使得,則

文獻

  • Atiyah, M.F. and Macdonald, I.G(1969). Introduction to Commutative Algebra. Addison-Wesley, Reading, MA.
  • Matsumura H., Commutative Algebra, 2nd ed. Benjamin/Cummings, 1980.

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