Non-Associative Rings

Posted byayushkhaitan3437Posted inUncategorized

I recently did a course on Associative Rings. Do there exist non-Associative rings? I’d like to discuss certain examples here.

I’m told that \Bbb{R}^3 is one such ring, which is non-associative under the operation of vector product. In other words, $A\times (B\times C)\neq (A\times B)\times C$.

After thinking about it for a bit, I found a supporting example in no time. We can see that i\times (i\times j)=-j. However, (i\times i)\times j=0.

Wikipedia says that Lie Algebras are also examples of non-Associative rings. But that is a topic for another time.

Published by ayushkhaitan3437

Hello! My name is Ayush Khaitan, and I'm a graduate student in Mathematics. I am always excited about talking to people about their research. Please please set up a meeting with me if you feel that I might have an interesting perspective to offer- https://calendly.com/ayushkhaitan/meeting-with-ayush

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