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| ``Re: "order of a ring" with a vengeance''
by Wkbj79 on 2007-06-01 14:26:32 |
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| Thanks a lot for these links. I have added a couple of these which I was able to verify.
I found this source interesting as well as a little odd:
http://www.michmaa.org/meeting03/abstracts.html
John Skukalek, Grand Valley State University
Rings of Small Order
Part of the abstract reads:
A standard topic in a first class in group theory is the classification of all groups of small order. The classification of rings of small order is more difficult due to the more complicated structure. In this session we will present a complete classification scheme for all rings of order 5 or less.
Part of my motivation for researching cyclic rings was that ring classification is typically not studied in a first course in abstract algebra, whereas group classification and field classification is. The thing that weirds me out is that this person only considers classification schemes for rings up to order 5. If you are going to investigate rings of order 4 (which can be difficult, but I did manage to prove that there are 11 of them), why not do the easy cases of order 6 and order 7 as well?
Also, after looking at this source:
http://home.wlu.edu/~dresdeng/smallrings/
I contacted Dr. Dresden. He said that he will read Cyclic Rings and let me know what he thinks. |
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