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
Preview
Unable to display preview. Download preview PDF.
References
I. G. Bashmakova and E. I. Slavutin, Algebra and algebraic number theory, in Mathematics of the 19th Century, ed. by A. N. Kolmogorov and A. P. Yushkevich, Birkhäuser, 1992, pp. 35–135.
G. Birkhoff, Current trends in algebra, American Math. Monthly 1973, 80: 760–782, and corrections in 1974, 81: 746.
N. Bourbaki, Elements of the History of Mathematics, Springer-Verlag, 1984.
L. Corry, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser, 1996.
H. M. Edwards, Fermat’s Last Theorem: A Genetic Introduction to Algebraic Number Theory, Springer-Verlag, 1977.
D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, 1995.
E. Galois, Sur la théorie des nombres. English translation in Introductory Modern Algebra: A Historical Approach, by S. Stahl, Wiley, 1997, pp. 277–284.
H. Hasse, History of class field theory, in Algebraic Number Theory, Proceedings of an Instructional Conference, ed. by J. Cassels & A. Fröhlich, Thompson Book Co., 1967, pp. 266–279.
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1982.
N. Jacobson, Basic Algebra I, II, W. H. Freeman, 1974 & 1980.
B. M. Kiernan, The development of Galois theory from Lagrange to Artin, Arch. Hist. Ex. Sc. 1971/72, 8: 40–154.
I. Kleiner, The roots of commutative algebra in algebraic number theory, Math. Mag. 1995, 68: 3–15.
D. Laugwitz, Bernhard Riemann, 1826–1866, Birkhäuser, 1999. (Translated from the German by A. Shenitzer.)
R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications,Cambridge University Press, 1986.
E. H. Moore, A doubly-infinite system of simple groups, New York Math. Soc. Bull. 1893, 3: 73–78.
W. Purkert, Zur Genesis des abstrakten Körperbegriffs I, II, NTM 1971, 8: 23–37 and 1973, 10: 8–20. (Unpublished English translation by A. Shenitzer.)
W. Purkert and H. Wussing, Abstract algebra, in Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, ed. by I. Grattan-Guinness, Routledge, 1994, vol. 1, pp. 741–760.
H. M. Pycior, George Peacock and the British origins of symbolical algebra, Hist. Math. 1981, 8: 23–45.
J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer-Verlag, 1992.
E. Steinitz, Algebraische Theorie der Körper, 2nd ed., Chelsea, 1950.
J.-P. Tignol, Galois’ Theory of Algebraic Equations, Wiley, 1988.
B. L. van der Waerden, Die Algebra seit Galois, Jahresbericht d. DMV 1966, 68: 155–165.
H. Weber, Die allgemeinen Grundlagen der Galois’schen Gleichungstheorie, Math. Ann. 1893, 43: 521–549.
D. Winter, The Structure of Fields, Springer-Verlag, 1974.
M. Scanlan, Who were the American postulate theorists?, Jour. of Symbolic Logic 1991, 56: 981–1002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Boston
About this chapter
Cite this chapter
Kleiner, I. (2007). History of Field Theory. In: Kleiner, I. (eds) A History of Abstract Algebra. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4685-1_4
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4685-1_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4684-4
Online ISBN: 978-0-8176-4685-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.