Does there exist an English translation of Steinitz' 1910 work "Algebraische Theorie der Körper"?
http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002167042
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1$\begingroup$ It's extremely unlikely, as in the case of most other classic papers and books of that era. The original long Crelle paper was later published in book form, but as far as I know never translated. In any case, the mathematics itself would need to be translated somewhat into modern language. Sometimes that's the most challenging task. $\endgroup$– Jim HumphreysJul 8, 2013 at 19:32
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$\begingroup$ @JimHumphreys: I only browsed this paper once, in fact in the context of an MO question, but was very surprised how close its exposition felt to what I am used to. So in this particular case there might not be much need for modernizing. To Drew Armstrong: why would you need a translation? If it is only something specific you might ask this directly. $\endgroup$– user9072Jul 8, 2013 at 20:26
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1$\begingroup$ @quid: I am interested in the paper mainly for its historical significance. In particular, I would like to know Steinitz' opinion on the matter of whether and how abstract fields can be classified. $\endgroup$– Drew ArmstrongJul 9, 2013 at 21:18
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$\begingroup$ Thank you for the explication of the motivation. I am afraid since this is not a request on a narrow aspect I cannot be of help, not knowing the paper in full. $\endgroup$– user9072Jul 9, 2013 at 23:04
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You may already know this, but the best reference about Steinitz $1910$ work I could find is the following summary by Peter Roquette: http://www.rzuser.uni-heidelberg.de/~ci3/STEINITZ.pdf. Some English references are given there, and apparently a lot of Steinitz $1910$ work can be found in the book "Modern Algenbra" by van der Waerden, but I don't know about a full translation.
Edit: I think, as Jim has pointed out, that most likely there is no translation. Certainly Peter Roquette would have mentioned a translation in his discussion, and I think he has searched for it.
answered Jul 8, 2013 at 19:21
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$\begingroup$ The Steinitz work: Algebraic Theory of Fields, which appeared in 1910 in the Journal for Pure and Applied Mathematics, has become since then the launch point for multiple and wide-ranging research thrusts in algebra and arithmetic. In its classic, beautiful and perfected depiction and with detailed derivations, it is not only a milestone inthe development of algebraic science but also still today a splendid and indispensable introduction for anyone who wishes to dedicate themselves to an in-depth study in this new algebraic discipline. $\endgroup$ Jul 11, 2023 at 6:54
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$\begingroup$ So it may appear justified, if we herewith fulfill a wish we have made many times, to make a new accessible edition of this work available to a wider public. $\endgroup$ Jul 11, 2023 at 6:54
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$\begingroup$ In order to secure the usefulness of this work as an introductory guide, we have added a set of clarifications which are gathered together in a section at the end. These further the aim, on the one hand to help with possible difficulties with the text and on the other hand also to make the developments where needed as simple as possible given the state of today's knowledge. There are in particular proofs in which well-ordering and the principle of transfinite induction play a role. $\endgroup$ Jul 11, 2023 at 6:56
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$\begingroup$ At such places these clarifications serve as substitutes for large parts of the text. In an appendix, we add an outline of Galois Theory. We believe that this is the correct place for such an appendix; for Galois Theory is really the principal subject of consideration aimed at in the second Steinitz article which was not fully developed by Steinitz himself. $\endgroup$ Jul 11, 2023 at 6:56
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$\begingroup$ The orginal Steinitz text is apart from minor technical details after removal of printing errors is given unchanged. The appendix and the clarifications were handled in the main by the junior author. We are indebted to the wife of the junior author who transcribed(?) the manuscript and read the corrections in full, further Fräulein stud. mat. Käte Kröncke who produce the index and Herr Dr. W. Franz who gave valuable advice on the corrections. $\endgroup$ Jul 11, 2023 at 6:57