Order, lattices, ordered algebraic structures Well-orders, well-founded orders, well-quasi-orders Concept
Descending chain condition
Summary
A partially ordered set satisfies the descending chain condition when every decreasing sequence of its elements is eventually constant. It is the dual of the ascending chain condition. Applied to the ideals of a ring, it defines Artinian rings; applied to submodules, it defines Artinian modules. For posets it is equivalent, under the axiom of dependent choice, to being a well-founded order.
Further reading
About this page
| Tag | 6SVWAP8WP5 |
|---|---|
| URI | m2://6SVWAP8WP5 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06, 13E10 |
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