Beyond class field theory: Helmut Hasse's arithmetic in the theory of algebras in early 1931

DOI10.1007/s00407-007-0001-yzbMath1128.01022OpenAlexW2034077769MaRDI QIDQ2457840

Joachim Schwermer, Della Dumbaugh Fenster

Publication date: 23 October 2007

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00407-007-0001-y

zbMATH Keywords

Hasse invariantnorm residue symbollocal-global principledivision algebranorm residueEmmy NoetherRichard Brauer

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60)

Cites Work

• Leonard Eugene Dickson and his work in the arithmetics of algebras
• Über \({\mathfrak p}\)-adische Schiefkörper und ihre Bedeutung für die Arithmetik hyperkomplexer Zahlsysteme
• A delicate collaboration: Adrian Albert and Helmut Hasse and the principal theorem in division algebras in the early 1930's.
• Die Struktur der R. Brauerschen Algebrenklassengruppe über einem algebraischen Zahlkörper. Insbesondere Begründung der Theorie des Normenrestsymbols und Herleitung des Reziprozitätsgesetzes mit nichtkommutativen Hilfsmitteln
• Beweis eines Hauptsatzes in der Theorie der Algebren.
• A Determination of All Normal Division Algebras Over an Algebraic Number Field
• Theory of Cyclic Algebras Over An Algebraic Number Field
• Knot Invariants in Vienna and Princeton during the 1920s: Epistemic Configurations of Mathematical Research
• The influence of J. H. M. Wedderburn on the development of modern algebra
• Class field theory -- its centenary and prospect. Proceedings of the 7th MSJ International Research Institute of the Mathematical Society of Japan, Tokyo, Japan, June 3--12, 1998
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