The Brauer-Hasse-Noether Theorem in Historical Perspective (Schriften der Mathematisch-naturwissenschaftlichen Klasse Book 15)

The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept at the Handschriftenabteilung of the University Library at Göttingen. Hasse had an extensive correspondence; he liked to exchange mathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical interest, searching through this treasure can help us to assess the development of Number Theory through the 1920s and 1930s. The present volume is largely based on the letters and other documents its author has found concerning the Brauer-Hasse-Noether Theorem in the theory of algebras; this covers the years around 1931. In addition to the documents from the literary estates of Hasse and Brauer in Göttingen, the author also makes use of some letters from Emmy Noether to Richard Brauer that are preserved at the Bryn Mawr College Library (Pennsylvania, USA). The Unpublished Writings Of Helmut Hasse, Consisting Of Letters, Manuscripts And Other Papers, Are Kept At The Handschriftenabteilung Of The University Library At Gottingen. Hasse Had An Extensive Correspondence; He Liked To Exchange Mathematical Ideas, Results And Methods Freely With His Colleagues. There Are More Than 8000 Documents Preserved. Although Not All Of Them Are Of Equal Mathematical Interest, Searching Through This Treasure Can Help Us To Assess The Development Of Number Theory Through The 1920s And 1930s. The Present Volume Is Largely Based On The Letters And Other Documents Its Author Has Found Concerning The Brauer-hasse-noether Theorem In The Theory Of Algebras; This Covers The Years Around 1931. In Addition To The Documents From The Literary Estates Of Hasse And Brauer In Gottingen, The Author Also Makes Use Of Some Letters From Emmy Noether To Richard Brauer That Are Preserved At The Bryn Mawr College Library (pennsylvania, Usa).--book Jacket. Introduction -- The Main Theorem : Cyclic Algebras -- The Paper : Dedication To Hensel -- The Local-global Principle -- From The Local-global Principle To The Main Theorem -- The Brauer Group And Class Field Theory -- The Team : Noether, Brauer And Hasse -- The American Connection : Albert -- Epilogue: Käte Hey. Peter Roquette. Includes Bibliographical References (p. [83]-90) And Index. Introduction....Pages 1-3 The Main Theorem: Cyclic Algebras....Pages 5-7 The Paper: Dedication to Hensel....Pages 9-13 The Local-Global Principle....Pages 15-24 From the Local-Global Principle to the Main Theorem....Pages 25-35 The Brauer Group and Class Field Theory....Pages 37-50 The Team: Noether, Brauer and Hasse....Pages 51-60 The American Connection: Albert....Pages 61-77 Epilogue: Käte Hey....Pages 79-81