I'm writing a paper on Emmy Noether for my introductory Abstract Algebra class, and I'm looking for examples of noncommutative Noetherian rings in which the Lasker-Noether theorem fails to hold.
According to the wikipedia article, Noether herself presented a counterexample, although it does not link to any information regarding an example. I can't read German, but maybe it's listed in her 1921 article somewhere?
I'm really just looking one or two simple examples, even if they weren't proposed by Noether herself.
All help is greatly appreciated. Thank you.
Here is the wikipedia article: http://en.wikipedia.org/wiki/Lasker%E2%80%93Noether_theorem
Here is her original paper: http://www.springerlink.com/content/m3457w8h62475473/