Abstract
THE existence of various systems of algebra, in which the commutative and associative laws of ordinary algebra are not assumed to be valid, has been known to mathematicians since Hamilton expounded his theory of quaternions. Such systems of non-commutative and non-associative algebra, based on a set of postulates consistent with itself, are now termed linear, and the general entity of a linear algebra, a hypercomplex number, marks the final stage in the evolution of number. The first half of Prof. Dickson's book expounds the theory of linear algebras and explains the terminology adopted in their classification. Only moderate mathematical attainments in the reader are assumed, and, apart from the development of the subject-matter, the book will be of great value to those interested in the foundations of mathematics.
Algebras and their Arithmetics.
By Prof. L. E. Dickson. (University of Chicago Science Series.) Pp. xii + 241. (Chicago: University of Chicago Press; London: Cambridge University Press, 1923.) 2.25 dollars.
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B., W. Algebras and their Arithmetics. Nature 114, 532 (1924). https://doi.org/10.1038/114532b0
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DOI: https://doi.org/10.1038/114532b0
