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A number having properties departing from those of the Real and Complex Numbers. The most common examples are Biquaternions, Exterior Algebras, Group algebras, Matrices, Octonions, and Quaternions.
References
van der Waerden, B. L. A History of Algebra from Al-Khwarizmi to Emmy Noether.
New York: Springer-Verlag, pp. 177-217, 1985.