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Ascending Chain Condition


The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant.

A module M fulfils the ascending chain condition if its set of submodules obeys the condition with respect to inclusion. In this case, M is called Noetherian.


See also

Descending Chain Condition, Noetherian Module, Noetherian Ring, 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

Ascending Chain Condition

Cite this as:

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

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