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Artinian Ring


A ring is called left (respectively right) Artinian if it does not contain an infinite descending chain of left (resp. right) ideals. In this case the ring in question is said to satisfy the descending chain condition on left (resp. right) ideals.

A ring is called Artinian if it is both left and right Artinian.


See also

Artinian Module, Descending Chain Condition, Left Ideal, Noetherian Ring, Right Ideal

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References

Artin, E. "Zur Theorie der hyperkomplexer Zahlen." Hamb. Abh. 5, 251-260, 1928.Artin, E. "Zur Arithmetik hyperkomplexer Zahlen." Hamb. Abh. 5, 261-289, 1928.Hungerford, T. W. Algebra, 8th ed. New York: Springer-Verlag, 1997.

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Artinian Ring

Cite this as:

Weisstein, Eric W. "Artinian Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArtinianRing.html

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