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单词 Krull Dimension
释义

Krull Dimension

If is a Ring (commutative with 1), the height of a Prime Ideal is defined as the Supremum ofall so that there is a chain where all are distinct PrimeIdeals. Then, the Krull dimension of is defined as the Supremum of all the heights of all itsPrime Ideals.

See also Prime Ideal


References

Eisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York: Springer-Verlag, 1995.

Macdonald, I. G. and Atiyah, M. F. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969.


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