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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Notes
- 1.
For a careful analysis of the book, see Corry (1996, pp. 40–45).
- 2.
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.
- 3.
As quoted in Kiernan (1971, p. 136).
- 4.
References
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)
Hawkins, T.: The Mathematics of Frobenius in Context. Springer, Berlin (2013)
Kiernan, B.M.: The development of Galois theory from Lagrange to Artin. Arch. Hist. Exact Sci. 8, 40–154 (1971)
Weber, H.: Die allgemeinen Grundlagen der Galois’schen Gleichungstheorie. Math. Ann. 43, 521–549 (1893)
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Gray, J. (2018). Algebra at the End of the Nineteenth Century. In: A History of Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-94773-0_22
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