Ascending chain condition on principal ideals

In abstract algebra, the ascending chain condition can be applied to the posets of principal left, principal right, or principal two-sided ideals of a ring, partially ordered by inclusion. The ascending chain condition on principal ideals is satisfied if there is no infinite strictly ascending chain of principal ideals of the given type (left/right/two-sided) in the ring, or said another way, every ascending chain is eventually constant.

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