MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
1

2

I am having trouble showing that a ring which is left Artinian and right Noetherian is right Artinian.

flag
Elohemahab: are you sure this stuff holds for noncommutative rings? – darij grinberg Mar 15 2011 at 21:32
For the title: Since [DCC] is stronger than ACC, a left (right) Artinian ring is also a left (right) Noetherian ring. Hence, you can take; for instance, rings for which left and right coincides such as finite rings and commutative rings. – To be cont'd Mar 15 2011 at 21:34
That is another homework problem. Voted to close. – Mark Sapir Mar 15 2011 at 21:45
2 
 Hint: Consider the $J$-adic filtration on the ring $A$, where $J$ is the Jacobson radical, and apply Artin-Wedderburn to $A/J$. – Konstantin Ardakov Mar 15 2011 at 22:33

closed as off topic by Mark Sapir, Will Jagy, Martin Brandenburg, Bruce Westbury, Tom Goodwillie Mar 16 2011 at 2:40

Browse other questions tagged or ask your own question.