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I am studying Introductory Algebraic Number Theory written by S. Alaca and K. Williams.

The authors mention the theorem concerning an integral basis for pure cubic fields but do not provide proof.

However, the original paper is not in English. The reference given in the book is

R. Dedekind, Uber die Anzahl der Idealklassen in reinen kubischen Zahlk ¨ orpern, ¨ Journal fur die reine und angewandte Mathematik 121 (1900), 40 ¨ –123. (Gesammelte Mathematische Werke II, pp. 148–233, Vieweg, Wiesbaden, 1931.

I am interested in reading the original paper. Where can I find the translation of this paper to the language of English (or a book containing the same theorem in English)?

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    $\begingroup$ I'm pretty sure this is done in the book "Number Fields" by Marcus, perhaps as a guided exercise (a very nice one). There is a new edition of that book, typed in latex. $\endgroup$
    – efs
    Commented Aug 20, 2021 at 14:25
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    $\begingroup$ Is the paper, Spearman & Williams, An explicit integral basis for a pure cubic field, Far East J Math Sci 6 (1) (1998) 1-14, people.math.carleton.ca/~williams/papers/pdf/216.pdf helpful? There's also a Missouri State University dissertation, Bieda, Kristen, "Integral Basis of Pure Cubic Fields" (2004). MSU Graduate Theses. 1612. bearworks.missouristate.edu/theses/1612 $\endgroup$
    – Gerry Myerson
    Commented Aug 21, 2021 at 2:28

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