Abstract
In this chapter, we look at the Kroneckerian alternative to Dedekind’s approach to ‘ring theory’ set out in his Grundzüge and later extended by the Hungarian mathematician Gyula (Julius) König. This leads us to the emergence of the concept of an abstract field.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Biermann, K.R.: Die Mathematik und ihre Dozenten an der Berliner Universität, 1810-1920. Stationen auf dem Wege eines mathematischen Zentrums von Weltgeltung. Akademie-Verlag, Berlin (1973/1988)
Edwards, H.M.: Divisor Theory. Birkhäuser, Boston (1990)
Klein, C.F.: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Springer, Berlin (1926–1927); Chelsea rep. New York
Kronecker, L.: In: K. Hensel (ed.) Vorlesungen über Zahlentheorie. Springer, Berlin (1901)
Landsberg, G.: Algebraische Gebilde. Arithmetische Theorie algebraischer Grössen. Encyclopädie der mathematischen Wissenschaften 1, 283–319 (1899)
Molk, J.: Sur une notion qui comprend celle de la divisibilité et la théorie générale de l’élimination. Acta Math. 6, 1–166 (1885)
Moore, G.H.: Zermelo’s Axiom of Choice. Its Origins, Development, and Influence. Studies in the History of Mathematics and Physical Sciences, vol. 8. Springer, Berlin (1982)
Netto, E.: Ueber die arithmetisch-algebraischen Tendenzen Leopold Kronecker’s. Chicago Congress Papers, pp. 243–257 (1896)
Neumann, P.M.: The concept of primitivity in group theory and the second memoir of Galois. Arch. Hist. Exact Sci. 60, 379–429 (2006)
Szénássy, B.: History of Mathematics in Hungary Until the 20th Century. Springer, Berlin (1992)
Weber, H.: Die allgemeinen Grundlagen der Galois’schen Gleichungstheorie. Math. Ann. 43, 521–549 (1893)
Weyl, H.: Algebraic Theory of Numbers. Annals of Mathematics Studies, vol. 1. Princeton University Press, Princeton (1940)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Gray, J. (2018). Kronecker’s Algebraic Number Theory. In: A History of Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-94773-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-94773-0_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94772-3
Online ISBN: 978-3-319-94773-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)