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Dedekind’s Later Theory of Ideals

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A History of Abstract Algebra

Part of the book series: Springer Undergraduate Mathematics Series ((SUMS))

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Abstract

In this chapter, we look at how Dedekind refined his own theory of ideals in the later 1870s, and then at the contrast with Kronecker

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Notes

  1. 1.

    See Avigad (2006).

  2. 2.

    See Corry (1996).

  3. 3.

    See the foreword to Dedekind (1964).

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)

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  • Corry, L.: Modern algebra and the rise of mathematical structures. Science Networks. Historical Studies, vol. 17, 2nd edn. 2004. Birkhäuser, Basel (1996)

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  • Dedekind, R.: Über die Theorie der ganzen algebraischen Zahlen. Nachdruck des elften Supplements (Lejeune-Dirichlet 1893) (1964); preface by B. L. van der Waerden, Vieweg, Braunschweig

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  • Hilbert, D.: Die Theorie der algebraischen Zahlkörper (Zahlbericht). Jahresbericht der Deutschen Mathematiker-Vereinigung 4, 175–546 (1897); in Gesammelte Abhandlungen 1, 63–363, transl. I. Adamson, The theory of algebraic number fields, Berlin, Springer, 1998

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Gray, J. (2018). Dedekind’s Later 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_18

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