Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system.
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As for mathematics, the hyperbolic quaternion is another hypercomplex number, as such structures were called at the time.
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The various hypercomplex numbers were identified with matrix rings by Joseph Wedderburn ( 1908 ) and Emil Artin ( 1928 ).
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Following William Kingdon Clifford who had extended quaternions to dual quaternions, McAulay made a special study of this hypercomplex number system.
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There was even a professional research association, the Quaternion Society, devoted to the study of quaternions and other hypercomplex number systems.
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On the other hand, the limitation of three dimensions in geometry was surpassed in the 19th century through considerations of parameter space and hypercomplex numbers.
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Karen Parshall has written a detailed exposition of the heyday of hypercomplex numbers, including the role of such luminaries as Theodor Molien and Eduard Study.
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For the transition to modern algebra, Bartel van der Waerden devotes thirty pages to hypercomplex numbers in his " History of Algebra ".
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Scheffers contributed a further short note, this time including reference to 1867 work by Edmond Laguerre on linear systems, a rich source of hypercomplex numbers.
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Muses also envisioned a mathematical number concept, Musean hypernumbers, that includes hypercomplex number algebras such as complex numbers and split-complex numbers as primitive types.
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