Non-Associative Rings

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: