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2018 | OriginalPaper | Chapter

22. Algebra at the End of the Nineteenth Century

Author : Jeremy Gray

Published in: A History of Abstract Algebra

Publisher: Springer International Publishing

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Abstract

In this chapter we begin to look at the major change that happened to algebra in the nineteenth century: the transformation from polynomial algebra to modern algebra. A vivid impression of the subject is given by the book that described the state of the art around 1900, Weber’s Lehrbuch der Algebra, much of which described Galois theory and number theory as it then stood.

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For a careful analysis of the book, see Corry (1996, pp. 40–45).

Weber explained that an equation was metacyclic when it was completely solvable by a chain of cyclic equations. It follows that the roots of such an equation are expressible in terms of nested radicals.

As quoted in Kiernan (1971, p. 136).

Quoted in Corry (1996, p. 128) from Dugac (1976, p. 269). On Frobenius, see Hawkins (2013).

Corry, L.: Modern algebra and the rise of mathematical structures. Science Networks. Historical Studies, vol. 17, 2nd edn. 2004. Birkhäuser, Basel (1996)

Dugac, P.: Richard Dedekind et les Fondements des Mathématiques. Vrin, Paris (1976)MATH

Hawkins, T.: The Mathematics of Frobenius in Context. Springer, Berlin (2013)CrossRef

Kiernan, B.M.: The development of Galois theory from Lagrange to Artin. Arch. Hist. Exact Sci. 8, 40–154 (1971)MathSciNetCrossRef

Weber, H.: Die allgemeinen Grundlagen der Galois’schen Gleichungstheorie. Math. Ann. 43, 521–549 (1893)MathSciNetCrossRef

Title: Algebra at the End of the Nineteenth Century
Author: Jeremy Gray
Publisher: Springer International Publishing
Book: A History of Abstract Algebra
Print ISBN: 978-3-319-94772-3

Electronic ISBN: 978-3-319-94773-0

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-94773-0_22

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