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You can introduce the imaginary unit , then you can introduce the quaternions. Now somebody has introduced n-imaginary units for sure, what is the term.

I want to read about it . Tell me. Please

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Look up octonions and sedenions. –  J. M. Oct 31 '11 at 19:02
    
en.wikipedia.org/wiki/Biquaternion –  Graphth Oct 31 '11 at 19:02
    
Please don't "sign" your messages. Your signature already appears in the bottom right of every post you make. –  Arturo Magidin Oct 31 '11 at 19:13
    
You might also be interested in reading about Clifford algebras. –  Hans Lundmark Oct 31 '11 at 20:13

1 Answer 1

There is the Cayley-Dickson construction, which in some sense continues the sequence indefinitely. However, the algebras become progressively less well-behaved beyond the first one or two steps. The quaternions are not commutative, and the next element in the series, the octonions, are not even associative!

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