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On a Theorem in Hypercomplex Numbers

Published online by Cambridge University Press:  15 September 2014

J. H. Maclagan-Wedderburn
J. H. Maclagan-Wedderburn
Affiliation:
Carnegie Research Fellow.
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Extract

Scheffers in the Mathematische Annalen, vol. xxxix., pp. 364–74, enunciates the following theorem:—If A is an algebra containing the quaternion algebra B as a subalgebra, and if A and B have the same modulus, A can be expressed in the form B C = A = C B, where C is a subalgebra of A every element of which is commutative with every element of B: in other words, if i1, i2, i3, i4 is a basis of B, it is possible to find an algebra C with the basis e1, e2, … ec, such that each of its elements is commutative with every element of B, and such that the elements eris(r = 1, 2, … c, S = 1, … 4) form a basis of A; and if a is the order of A, then a = 4c.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 26 , Issue 1 , 1906 , pp. 48 - 50
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

* American Journal, vol. i., pp. 350–58.