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Platonov, V. P.; Rapinchuk, A. S.

The multiplicative structure of division rings over number fields and the Hasse norm principle. (English) Zbl 0579.12010

Proc. Steklov Inst. Math. 165, 187-205 (1985).
Translation from Tr. Mat. Inst. Steklova 165, 171-187 (Russian) (1984; Zbl 0559.12010).

Cited in 1 Review

MSC:

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

Keywords:

multiplicative structure; skew fields over number fields; Hasse; norm principle; algebraic group; group of rational points; quadratic forms; Skolem-Noether theorem; algebra of quaternions; class field theory; direct subgroup; Spin(f); SL(1,D); trace

Citations:

Zbl 0423.22015; Zbl 0070.258; Zbl 0386.20019; Zbl 0289.16007; Zbl 0431.12012; Zbl 0503.12011; Zbl 0559.12010
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