A delicate collaboration: Adrian Albert and Helmut Hasse and the principal theorem in division algebras in the early 1930's.
type: Item
instance of: scholarly article
title: A delicate collaboration: Adrian Albert and Helmut Hasse and the principal theorem in division algebras in the early 1930's.
zbMATH Open document ID: 1066.01026
author: Joachim Schwermer
author: Della Dumbaugh Fenster
published in: Archive for History of Exact Sciences
publication date: 2005-06-09T00:00:00Z
review text: The 1932 volume of the \textit{Transactions of the American Mathematical Society} contains a joint paper of A. A. Albert (1905--1972) and H. Hasse (1898--1979) on the structural description of a normal division algebra over an algebraic number field [cf. Trans. Am. Math. Soc. 34, 722--726 (1932; Zbl 0005.05003 and JFM 58.0144.02)]. This was during a period of intense, but independent, mathematical activity in the United States and Germany on linear algebras. On the American side were J. H. M. Wedderburn, L. E. Dickson and Albert, while in Europe, E. Noether, R. Brauer and Hasse collaborated, eventually producing a joint paper in 1932 [J. Reine Angew. Math. 167, 399--404 (1932; Zbl 0003.24404 and JFM 58.0142.03)]. On 6 February, 1931, in response to an enquiry from Hasse about his work, Albert sent the first of ten letters over a period of 14 months discussed in this article. Each man became apprised of the work of the other, with Albert offering advice on plugging a gap in the Brauer-Hasse-Noether paper. In addition, they worked on an alternative approach. The delicacy of the collaboration lies in the question of the extent to which Albert felt his contribution to the German paper should be recognized, an issue handled with tact from both sides. The author outlines the careers of both men and describes the mathematical developments leading up to their exchange of letters.
reviewed by: Edward J. Barbeau
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A80
Mathematics Subject Classification ID: 16-03
zbMATH DE Number: 2174554
zbMATH Keywords: division algebra
zbMATH Keywords: linear algebras
zbMATH Keywords: number field
MaRDI profile type: Publication
full work available at URL: s00407-004-0093-6
OpenAlex ID: W2065290556
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DOI: 10.1007/S00407-004-0093-6
description: scientific article; zbMATH DE number 2174554