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In mathematics, Artinian is an adjective that describes objects that satisfy particular cases of the descending chain condition.
A ring is an Artinian ring if it satisfies the descending chain condition on ideals.
A module is an Artinian module if it satisfies the descending chain condition on submodules.
The concept is named for Emil Artin, who classified all simple rings whose one-sided ideals satisfy the descending chain condition.
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