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.
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.
