Abstract
One of the successes of Dedekind’s theory was the way it allowed Gauss’s very complicated theory of the composition of quadratic forms to be re-written much more simply in terms of modules and ideals in a quadratic number field, which in turn explained the connection between forms and algebraic numbers. In this chapter, we look at how this was done.
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Notes
- 1.
I have decided to concentrate on the fourth edition (1879) rather than the third (1879) because the fourth edition was reprinted in Dedekind’s Mathematische Werke.
References
Dedekind, R.: Sur la théorie des nombres entiers algébriques. Bull. sci. math. 1, 17–41 (1877); 69–92; 114–164; 207–248, and separately published, Gauthier-Villars, Paris, transl. J. Stillwell as Theory of Algebraic Integers, Cambridge U.P. 1996
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Gray, J. (2018). Quadratic Forms and Ideals. In: A History of Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-94773-0_19
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DOI: https://doi.org/10.1007/978-3-319-94773-0_19
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