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Artinian

In mathematics, a ring is Artinian if it has the descending chain condition on the poset of ideals under inclusion.

An algebra over a field that is finite-dimensional (over the field) is certainly Artinian, since any ideal must be a vector subspace. Any finite ring must be Artinian, also. Therefore the theory of Artinian rings (named for Emil Artin) has many classical examples.





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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Artinian".