Ascending Chain Condition

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

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

See also

Descending Chain Condition, Noetherian Module, Noetherian Ring, Partially Ordered Set, Sequence

This entry contributed by Margherita Barile

Explore with Wolfram|Alpha

More things to try:

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

Subject classifications