Abstract
This chapter picks up from the previous one and looks at how Dedekind analysed the concept of primality in an algebraic number field. This was to mark the start of a sharp difference of opinion with Kronecker.
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References
Avigad, J.: Methodology and metaphysics in the development of Dedekind’s theory of ideals. In: Ferreirós, J., Gray, J.J. (eds.) The Architecture of Modern Mathematics, pp. 159–186. Oxford University Press, New York (2006)
Corry, L.: Modern algebra and the rise of mathematical structures. Science Networks. Historical Studies, vol. 17, 2nd edn. 2004. Birkhäuser, Basel (1996)
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
Edwards, H.M.: Divisor Theory. Birkhäuser, Boston (1990)
Kronecker, L.: Grundzüge einer arithmetischen Theorie der algebraischen Grössen. Festschrift Reimer, Berlin (1882); and Journal für Mathematik 92, 1–123, in Werke 2, 237–388
Reed, D.: Figures of Thought: Mathematics and Mathematical Texts. Routledge, London (1994)
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Gray, J. (2018). Dedekind’s First Theory of Ideals. In: A History of Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-94773-0_17
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DOI: https://doi.org/10.1007/978-3-319-94773-0_17
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