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Jul 11, 2023 at 6:57 comment added idontgetoutmuch 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.
Jul 11, 2023 at 6:56 comment added idontgetoutmuch 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.
Jul 11, 2023 at 6:56 comment added idontgetoutmuch 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.
Jul 11, 2023 at 6:54 comment added idontgetoutmuch 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.
Jul 11, 2023 at 6:54 comment added idontgetoutmuch 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.
Aug 9, 2018 at 21:05 vote accept Drew Armstrong
Jul 10, 2013 at 8:10 history edited Dietrich Burde CC BY-SA 3.0
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Jul 8, 2013 at 19:21 history answered Dietrich Burde CC BY-SA 3.0