The multiplicative structure of division rings over number fields and the Hasse norm principle

zbMath0579.12010MaRDI QIDQ1066952

Andrei S. Rapinchuk, Vladimir Platonov

Publication date: 1985

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

tracequadratic formsgroup of rational pointsnorm principlealgebraic groupalgebra of quaternionsclass field theorySkolem-Noether theoremmultiplicative structuredirect subgroupHasseskew fields over number fieldsSL(1,D)Spin(f)

Mathematics Subject Classification ID

Rational points (14G05) Linear algebraic groups over global fields and their integers (20G30) Class field theory (11R37) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Algebras and orders, and their zeta functions (11S45)

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