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In mathematics, a left quaternionic vector space is a left H-module where H is the division ring of quaternions.
The space H of n-tuples of quaternions is both a left and right H-module using the componentwise left and right multiplication:
for quaternions q and q1, q2,... qn.
Since H is a division algebra, every finitely generated H-module has a basis, and hence is isomorphic to H for some n.
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