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What is the characteristic of the ring of quaternions
Solution
Quaternions are a number system that extends to complex numbers
Thus quaternions will have not only real numbers but also complex numbers.
Normally the elements will be {-1,-i,-j,-k,1,i,j,k} with Cayley table as
Multiplicative identity is 1.
Additive identity =0
Characteristic is n such that
1+1+1+...+1 n times =0
(Since it is not possible to have as above, n is undefined.x1ijk11ijkii-1k-jjj-k-1ikkj-1-i

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What is the characteristic of the ring of quaternionsSolutionQ.pdf

  • 1. What is the characteristic of the ring of quaternions Solution Quaternions are a number system that extends to complex numbers Thus quaternions will have not only real numbers but also complex numbers. Normally the elements will be {-1,-i,-j,-k,1,i,j,k} with Cayley table as Multiplicative identity is 1. Additive identity =0 Characteristic is n such that 1+1+1+...+1 n times =0 (Since it is not possible to have as above, n is undefined.x1ijk11ijkii-1k-jjj-k-1ikkj-1-i