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Descending Chain Condition

The descending chain condition, commonly abbreviated "D.C.C.," is the dual notion of the ascending chain condition. The descending chain condition for a partially ordered set X requires that all decreasing sequences in X become eventually constant.

A module fulfilling the descending chain condition is called Artinian.

See also

Artinian Module, Artinian Ring, Ascending Chain Condition, Partially Ordered Set, Sequence

This entry contributed by Margherita Barile

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References

Atiyah, M. F. and Macdonald, I. G. Introduction to Commutative Algebra. Menlo Park, CA: Addison-Wesley 1969.

Referenced on Wolfram|Alpha

Descending Chain Condition

Cite this as:

Barile, Margherita. "Descending Chain Condition." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DescendingChainCondition.html

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